Recent papers and preprints
- Bobkov, S. G.
Fisher-type information involving higher order derivatives.
Preprint (2024).
- Bobkov, S. G.; Götze, F.
Rényi divergences in central limit theorems: old and new.
Preprint (2024).
- Bobkov, S. G.; Ledoux, M.
Fourier analytic bound for Zolotarev distances, and applications
to empirical measures.
Preprint (2024).
- Bobkov, S. G.
Zolotarev-type distances.
Preprint (2023).
- Bobkov, S. G.; Duggal, D.
Spherical covariance representations.
Preprint (2023).
- Bobkov, S. G.; Duggal, D.
Höffding's kernels and periodic covariance representations.
Preprint (2023).
- Barki, A.; Bobkov, S. G.; Dagher, E. B.; Roberto, C.
Exponential inequalities in probability spaces revisited.
Preprint (2024).
- Bobkov, S. G.; Götze, F.
Esscher transform and the central limit theorem.
Preprint (2024).
- Bobkov, S. G.; Götze, F.
Berry-Esseen bounds in the local limit theorem.
Preprint (2024).
- Bobkov, S. G.; Götze, F.
Central limit theorem for Rényi divergence of infinite order.
Preprint (2024), to appear in Ann. Probab.
- Bobkov, S. G.; Roberto, C.
Entropic isoperimetric inequalities for generalized Fisher information.
Preprint (2023). To appear in a Special Issue of PAFA dedicated to Professor
Vladimir Mazya.
- Bobkov, S. G.
On the remainder term in the approximate Fourier inversion formula.
J. Math. Sciences (NY), 281 (2024), no. 4, pp. 566-583.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Strictly subgaussian probability distributions.
Electronic J. Probab. 29 (2024), article no. 62, pp. 1-28.
- Bobkov, S. G.; Volzone, B.
On Gilles Pisier's approach to Gaussian concentration, isoperimetry, and
Poincaré-type inequalities.
Electronic J. Probab. 29 (2024), article no. 45, pp. 1-27.
Recent papers and preprints
Books, surveys
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Concentration and Gaussian approximation for randomized sums (Preface and contents).
Probab. Theory Stoch. Model., 104 Springer, Cham, 2023, xvii+434 pp.
- Bobkov, S. G.; Ledoux, M.
One-dimensional empirical measures, order statistics and
Kantorovich transport distances.
Memoirs of the AMS 261 (2019), no. 1259, v+126 pp.
- Bobkov, S. G.
Asymptotic expansions for products of characteristic functions under moment
assumptions of non-integer orders.
The IMA Volumes in Mathematics and its Applications. Concentration,
Convexity and Discrete Structures, 161 (2017), pp. 297-357.
- Bobkov, S. G.
Proximity of probability distributions in terms of Fourier-Stieltjes
transforms.
Russian Math. Surveys, vol. 71, issue 6 (2016), pp. 1021-1079.
Translated from: Uspekhi Matem. Nauk, vol. 71, issue 6 (432), 2016, pp. 37-98.
Russian version is
here.
- Bobkov, S. G.
Isoperimetric problems in the theory of infinite dimensional
probability measures. (Russian) LAMBERT Academic Publishing,
Saarbrucken, 2016, 312 pp.
- Bobkov, S. G.; Zegarlinski, B.
Entropy bounds and isoperimetry.
Mem. Amer. Math. Soc. 176 (2005), no. 829, x+69 pp.
- Bobkov, S. G.; Houdré, C.
Some connections between isoperimetric and Sobolev-type inequalities.
Mem. Amer. Math. Soc. 129 (1997), no. 616, viii+111 pp.
Recent papers and preprints
Papers
2018-2019
2022-2023
- Bobkov, S. G.
Decay of convolved densities via Laplace transform.
Ann. Probab. 51 (2023), no. 5, pp. 1603-1615.
- Bobkov, S. G.
Refinements of Berry-Esseen inequalities in terms of Lyapunov coefficients.
J. Fourier Anal. Appl. 29:72 (2023), 33 pp.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Richter's local limit theorem, its refinement, and related results.
Lithuanian Math. J. 63 (2023), no. 2, pp. 138-160.
- Bobkov, S. G.; Roberto, C.
Entropic isoperimetric inequalities.
High Dimensional Probability IX, Progress in Probability, Birkhauser/Springer,
80 (2023), pp. 97-121.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Asymptotic expansions and two-sided bounds in randomized central limit theorems.
Geometric Aspects of Functional Analysis, Lecture Notes in Math.
2327 (2023), pp. 67-128.
- Bobkov, S. G.; Roberto, C.
On sharp Sobolev-type inequalities for multidimensional Cauchy measures.
Geometric Potential Analysis. Advances in Analysis and Geometry
6 (2022), pp. 135–152, De Gruyter, Berlin.
- Bobkov, S. G.
Upper bounds for the Fisher information.
Electronic J. Probab. 27 (2022), article no. 115, pp. 1-44.
- Bobkov, S. G.; Marsiglieti, A.; Melbourne, J.
Concentration functions and entropy bounds for discrete log-concave distributions.
Combinatorics, Probability and Computing 31 (2022), pp. 54–72.
- Bobkov, S. G.; Ulyanov, V. V.
The Chebyshev-Edgeworth correction in the central limit theorem
for integer-valued independent summands.
Theory Probab. Appl. 66 (2022), no. 4, pp. 537–549.
Translation from: Teoriya Veroyatnostei i ee Primeneniya 66 (2021), pp. 676–692.
2018-2019
2020-2021
- Bobkov, S. G.; Ledoux, M.
A simple Fourier analytic proof of the AKT optimal matching theorem.
Annals Applied Probab. 31 (2021), no. 6, pp. 2567-2584.
- Bobkov, S. G.; Marsiglietti, A; Melbourne, J.
Concentration functions and entropy bounds for discrete log-concave distributions.
Probability and Computing. Cambridge University Press, 27 May 2021, pp. 1-19.
- Bobkov, S. G.; Danshina, M. A.; Ulyanov, V. V.
On rate of convergence to the Poisson law of the number of cycles in
the generalized random graphs.
Operator theory and harmonic analysis—OTHA 2020. Part II. Probability-analytical models,
methods and applications, 109–133, Springer Proc. Math. Stat., 358, Springer, Cham, 2021.
- Bobkov, S. G.; Naumov, A. A.; Ulyanov, V. V.
Two–sided bounds for PDFs maximum of a sum of weighted chi-square variables.
Recent developments in stochastic methods and applications, 178–189,
Springer Proc. Math. Stat., 371, Springer, Cham, 2021.
- Bobkov, S. G.; Ledoux, M.
Transport inequalities on Euclidean spaces for non-Euclidean metrics.
J. Fourier Anal. Appl. 26 (2020), no. 4, paper no. 60, 27 pp.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Poincaré inequalities and normal approximation for weighted sums.
Electron. J. Probab. 25 (2020), paper no. 155, 31 pp.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Normal approximation for weighted sums under a second-order correlation condition.
Ann. Probab. 48 (2020), no. 3, pp. 1202–1219.
- Bobkov, S. G.
Edgeworth corrections in randomized central limit theorems.
Geometric Aspects of Functional Analysis, Lecture Notes in Math.
2256 (2020), pp. 71–97.
- Bobkov, S. G.; Marsiglietti. A.
Entropic CLT for smoothed convolutions, and associated entropy bounds.
International Mathematics Research Notices IMRN 2020, no. 21, pp. 8057–8080.
- Bobkov, S. G.; Marsiglietti. A.
Local limit theorems for smoothed Bernoulli and other convolutions.
Teor. Veroyatn. Primen. 65 (2020), no. 1, pp. 79–102;
reprinted in: Theory Probab. Appl. 65 (2020), no. 1, pp. 62–81.
2018-2019
2018-2019
- Bobkov, S. G.
Local limit theorems for densities in Orlicz spaces.
J. Math. Sci. (N.Y.) 242 (2019), no. 1, pp. 52-68. Translated from:
Problems in mathematical analysis, no. 98 (2019), pp. 45-58.
- Bobkov, S. G.
Moments of the scores.
IEEE Transactions on Information Theory 65 (2019), no. 9, pp. 5294–5301.
- Bobkov, S. G.
Khinchine's theorem and Edgeworth approximations for
weighted sums. Ann. Statistics 47 (2019), no. 3, pp. 1616-1633.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Nonuniform bounds in the Poisson approximation with applications to
informational distances. II.
Lith. Math. J. 59 (2019), no. 4, pp. 469–497.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Non-uniform bounds in the Poisson approximation with applications to
informational distances I.
IEEE Trans. Inform. Theory 65 (2019), no. 9, pp. 5283–5293.
- Bobkov, S. G.; Marsiglietti. A.
Asymptotic behavior of Renyi entropy in the central limit theorem.
Progress in Probab., High
Dimensional Probability VIII. The Oaxaca Volume, 74 (2019), pp. 169–200.
- Bobkov, S. G.; Gozlan, N.; Roberto, C.; Samson, P.-M.
Polar isoperimetry. I: The case of the plane.
Progress in Probab., High
Dimensional Probability VIII. The Oaxaca Volume, 74 (2019), pp. 21–31.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Rényi divergence and the central limit theorem.
Ann. Probab. 47 (2019), no. 1, pp. 270-323.
- Bobkov, S. G.; Götze, F.; Sambale, H.
Higher order concentration of measure.
Communications in Comtemporary Mathematics. 21 (2019), no. 3, 1850043, 36 pp.
- Bobkov, S. G.; Klartag, B.; Koldobsky, A.
Estimates for moments of general measures on convex bodies.
Proceedings of the AMS, 146 (2018), no. 11, pp. 4879–4888.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Berry-Esseen bounds for typical weighted sums.
Electron. J. Probab. 23 (2018), no. 92, 22 pp.
- Bobkov, S. G.
Berry-Esseen bounds and Edgeworth expansions in the central limit theorem
for transport distances. Probab. Theory Related Fields 170 (2018),
pp. 229-262.
- Bobkov, S. G.
Central limit theorem and Diophantine approximations.
Journal Theor. Probab. 31 (2018), issue 4, pp. 2390-2411.
2016-2017
2016-2017
- Bobkov, S. G.; Marsiglietti. A.
Variants of Entropy Power Inequality.
IEEE Transactions on Information Theory 63 (2017), no. 12, pp. 7747-7752.
- Bobkov, S. G.; Nayar, P.; Tetali, P.
Concentration properties of restricted measures with
applications to non-Lipschitz functions.
Geometric Aspects of functional analysis,
Lecture Notes in Math. 2169 (2017), pp. 25-53.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Gaussian mixtures and normal approximation for V.N.Sudakov's typical
distributions.
Zap. nauchn. semin. POMI 457 (2017), Veroyatnost i Statistika. 25, pp. 37-52.
- Bobkov, S. G.
On isoperimetric functions of probability measures having log-concave densities
with respect to the standard normal law.
The IMA Volumes in Mathematics and its Applications. Concentration,
Convexity and Discrete Structures, 161 (2017), pp. 577-583.
- Bobkov, S. G.; Melbourne, J.
Hyperbolic measures on infinite dimensional spaces.
Probab. Surveys 13 (2016), pp. 57-88.
- Bobkov, S. G.; Cordero-Erausquin, D.
K-L-S-type isoperimetric bounds for log-concave probability measures.
Annali di Matematica Pura ed Applicata 195 (2016), pp. 681-695.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Second order concentration on the sphere.
Communications in Comtemporary Mathematics. Online 13 September 2016.
An extended version is
here.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Stability of Cramer's characterization of the normal law in
information distances.
In: High Dimensional Probability VII: The Cargese volume.
Progress in Probability 71 (2016), pp. 3-35.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Regularized distributions and entropic stability of Cramer's
characterization of the normal law.
Stochastic Processes Appl. 126 (2016), issue 12, pp. 3865-3887.
An extended version is
here.
2014-2015
2014-2015
- Bobkov, S. G.; Melbourne, J.
Localization for infinite dimensional hyperbolic measures.
(Russian) Doklady Akademii Nauk, vol. 462 (2015), no. 3, pp. 261-263.
English version [Doklady Mathematics, vol. 91 (2015), no. 3, pp. 297-299] is
here.
- Bobkov, S. G.; Chistyakov, G. P.
Entropy power inequality for the Rényi entropy.
IEEE Transactions on Information Theory 61 (2015), no. 2, pp. 708-714.
- Bobkov, S. G.; Ding, Y.
Optimal transport and Rényi informational divergence.
Electron. Comm. Probab. 20 (2015), no. 4, pp. 1-12.
- Bobkov, S. G.; Chistyakov, G. P.; Kösters, H.
The entropic Erdös-Kac limit theorem.
J. Theor. Probab. 28 (2015), no. 4, pp. 1520-1555.
- Bobkov, S. G.; Chistyakov, G. P.
On concentration functions of random variables.
J. Theor. Probab. 28 (2015), no. 3, pp. 976-988.
- Bobkov, S. G.; Gozlan, N.; Roberto, C.; Samson, P.-M.
Bounds on the deficit in the logarithmic Sobolev inequality.
J. Funct. Anal. 267 (2014), no. 11, pp. 4110–4138.
- Bobkov, S. G.; Colesanti, A; Fragalà, I.
Quermassintegrals of quasi-concave functions and generalized
Prekopa-Leindler inequalities.
Manuscripta Mathematica 143 (2014), no. 1-2, pp. 131-169.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Fisher information and convergence to stable laws.
Bernoulli (2014), no. 3, pp. 1620-1646.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Fisher information and the central limit theorem.
Probab. Theory Related Fields 159 (2014), issue 1-2, pp. 1-59.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Berry-Esseen bounds in the entropic central limit theorem.
Probab. Theory Related Fields 2014 (159), pp. 435-478.
- Bobkov, S. G.; Chistyakov, G. P.
Bounds on the maximum of the density for sums of independent random
variables.
J. Math. Sciences (New York), vol. 199 (2014), no. 2, pp. 100-106.
Translated from: Zapiski Nauchn. Semin. POMI, 408 (2012), Veroyatnost' i Statistika.
18, pp. 62-73.
Russian version is
here.
2012-2013
2012-2013
- Bobkov, S. G.
Entropic approach to E. Rio's central limit theorem for W_2 transport
distance.
Statistics and Probability Letters, 83 (2013), no. 7, pp. 1644–1648.
- Bobkov, S. G.; Madiman, M.
On the problem of reversibility of the entropy power inequality.
In: Limit Theorems in Probability, Statistics and Number Theory.
Springer Proceedings in Mathematics and Statistics, 42 (2013), pp. 61-74.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Rate of convergence and Edgeworth-type expansion in the entropic central limit
theorem.
Ann. Probab. 41 (2013), no. 4, pp. 2479-2512.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Convergence to stable laws in relative entropy.
J. Theor. Probab. 26 (2013), no. 3, pp. 803-818.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Stability problems in Cramér-type characterization in case of i.i.d. summands.
Theory Probab. Appl. 57 (2013), no. 4, 568-588.
Probab. Theory Appl. 57 (2012), no.4, pp.701–723.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Bounds for characteristic functions in terms of quantiles and entropy.
Electron. Comm. Probab. 17 (2012), electronic, No. 21, 9 pp.
- Bobkov, S. G.; Madiman, M.
An equipartition property for high-dimensional log-concave distributions.
Proc.of the 50th Annual Allerton Conference on Communication,
Control, and Computing, 2012.
- Bobkov, S. G.; Madiman, M.
Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures.
J. Funct. Anal. 262 (2012), no. 7, pp. 3309-3339.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Entropic instability of Cramer's characterization of the normal law.
Selected Works of Willem van Zwet, pp. 231-242,
Sel. Works Probab. Stat., Springer, New York, 2012.
2011
2011
- Bobkov, S. G.
The Brunn-Minkowski inequality in spaces with bitriangular laws of composition.
J. Math. Sciences (New York), vol. 179 (2011), no. 1, pp. 2-6.
Translated from: Problems in Math. Analysis, 61 (2011), pp. 5–8.
- Bobkov, S. G.
On Milman's ellipsoids and M-position of convex bodies.
In: Concentration, Functional Inequalities and Isoperimetry. Proceedings of the
International workshop, Contemporary Math., AMS, vol. 545, pp. 23-33, 2011.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Non-uniform bounds in local limit theorem in case of fractional moments. II.
Math. Methods of Statistics, vol. 20 (2011), no. 4, pp. 269-287.
- Bobkov, S. G.; Chistyakov, G. P.; Götze, F.
Non-uniform bounds in local limit theorem in case of fractional moments. I.
Math. Methods of Statistics, vol. 20 (2011), no. 3, pp. 171-191.
- Bobkov, S. G.; Madiman, M.; Wang, L.
Fractional generalizations of Young and Brunn-Minkowski inequalities.
In: Concentration, Functional Inequalities and Isoperimetry. Proceedings of the
International workshop, Contemporary Math., AMS, vol. 545, pp. 35-53, 2011.
- Bobkov, S. G.; Madiman, M.
Dimensional behaviour of entropy and information.
C. R. Math. Acad. Sci. Paris, 349 (2011), no. 3-4, pp. 201–204.
- Bobkov, S. G.; Madiman, M.
The entropy per coordinate of a random vector is highly constrained under convexity
conditions.
IEEE Transactions on Information Theory, vol. 57 (2011), no. 8, pp. 4940-4954.
- Bobkov, S. G.; Madiman, M.
Concentration of the information in data with log-concave distributions.
Ann. Probab. 39 (2011), no. 4, pp. 1528–1543.
2010
2010
- Bobkov, S. G.; Madiman, M.
Entropy and the hyperplane conjecture in convex geometry.
Information Theory Proceedings (ISIT), 2010 IEEE International Symposium,
Austin, Texas, 2010, pp. 1438-1442.
- Bobkov, S. G.
Gaussian concentration for a class of spherically invariant measures.
J. Math. Sciences (New York), vol. 167 (2010), no. 3, pp. 326-339.
Translated from: Problems in Math. Analysis, 46 (2010), pp. 45–56.
Russian version is
here.
- Bobkov, S. G.
The growth of L^p norms in presence of logarithmic Sobolev inequalities.
Vestnik Syktyvkar Univ., Ser. 1 (2010), no. 11, pp. 92-111.
- Bobkov, S. G.
Convex bodies and norms associated to convex measures.
Probab. Theory Related Fields, 147 (2010), no. 1-2, pp. 303–332.
- Bobkov, S. G.; Götze, F.; Tikhomirov, A. N.
On concentration of empirical measures and convergence to the semi-circle law.
J. Theor. Probab. 23 (2010), no. 3, pp. 792–823.
- Bobkov, S. G.; Götze, F.
Concentration of empirical distribution functions with applications to non-i.i.d. models.
Bernoulli, 16 (2010), no. 4, pp. 1385–1414.
- Bobkov, S. G.
Perturbations in the Gaussian isoperimetric inequality.
J. Math. Sciences (New York), vol. 166 (2010), no. 3, pp. 225-238.
Translated from: Problems in Math. Analysis, 45 (2010), pp. 3-14.
Russian version is
here.
- Bobkov, S. G.
On concentration of measure on the cube.
J. Math. Sciences (New York), vol. 165 (2010), no. 1, pp. 60-70.
Translated from: Problems in Math. Analysis, 44 (2010), pp. 55-64.
Russian version is
here.
- Bobkov, S. G.; Zegarlinski, B.
Distributions with slow tails and ergodicity of Markov semigroups in infinite
dimensions.
Around the research of Vladimir Maz'ya. I, pp. 13-79, Int. Math. Ser. (N. Y.),
11, Springer, New York, 2010.
2007-2009
2007-2009
- Bobkov, S. G.
On a theorem of V. N. Sudakov on typical distributions.
(Russian) J. Math. Sciences (New York), vol. 167 (2010), no. 4, pp. 464-473.
Translated from: Zap. Nauchn. Semin. POMI, vol. 368 (2009), pp. 59-74.
Russian version is
here.
- Bobkov, S. G.; Ledoux, M.
On weighted isoperimetric and Poincare-type inequalities.
IMS Collections. High Dimensional Probability V: The Luminy Volume.
Vol. 5 (2009), pp. 1–29.
- Bobkov, S. G.; Ledoux, M.
Weighted Poincaré-type inequalities for Cauchy and other convex measures.
Ann. Probab. 37 (2009), no. 2, pp. 403–427.
- Bobkov, S. G.; Götze, F.; Tikhomirov, A. N.
On the concentration of high dimensional matrices with randomly signed entries.
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 364
(2009), Veroyatnost i Statistika. 14.2, pp. 32–69.
- Bobkov, S. G.
On the isoperimetric constants for product measures.
J. Math. Sci. (N.Y.), vol. 159 (2009), no. 1, pp. 47–53.
Translated from: Problems in Math. Analysis, 40 (2009), pp. 49–56.
- Bobkov, S. G.; Götze, F.
Hardy type inequalities via Riccati and Sturm-Liouville equations.
Sobolev spaces in mathematics. I, pp. 69–86, Int. Math. Ser. (N. Y.), 8, Springer,
New York, 2009.
- Bobkov, S. G.
A note on the distributions of the maximum of linear Bernoulli processes.
Electron. Commun. Probab. 13 (2008), pp. 266–271.
- Bobkov, S. G.; Ledoux, M.
From Brunn-Minkowski to sharp Sobolev inequalities.
Ann. Mat. Pura Appl. (4) 187 (2008), no. 3, pp. 369–384.
- Bobkov, S. G.; Nazarov, F. L.
Sharp dilation-type inequalities with fixed parameter of convexity.
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 351 (2007),
Veroyatnost i Statistika. 12, pp. 54-78. Translation in J. Math. Sci. (N. Y.) 152 (2008),
no. 6, pp. 826–839.
- Bobkov, S. G.
On isoperimetric constants for log-concave probability distributions.
Geometric aspects of functional analysis, pp. 81–88, Lecture Notes in Math., 1910,
Springer, Berlin, 2007.
- Bobkov, S. G.
A remark on the surface Brunn-Minkowski-type inequality.
Geometric aspects of functional analysis, pp. 77–79, Lecture Notes in Math., 1910,
Springer, Berlin, 2007.
- Bobkov, S. G.
Large deviations and isoperimetry over convex probability measures with heavy tails.
Electr. J. Probab. 12 (2007), pp. 1072-1100.
- Bobkov, S. G.; Götze, F.
Concentration inequalities and limit theorems for randomized sums.
Probab. Theory Related Fields, 137 (2007), no. 1-2, pp. 49–81.
2003-2006
2003-2006
- Bobkov, S. G; Tetali, P
Modified logarithmic Sobolev inequalities in discrete settings.
J. Theoret. Probab. 19 (2006), no. 2, pp. 289–336.
- Bobkov, S. G.; Houdré, C.; Tetali, P.
The subgaussian constant and concentration inequalities.
Israel J. Math. 156 (2006), pp. 255–283.
- Bobkov, S. G.
Generalized symmetric polynomials and an approximate de Finetti representation.
J. Theoret. Probab. 18 (2005), no. 2, pp. 399–412.
- Bobkov, S. G.
Concentration of normalized sums and a central limit theorem for noncorrelated
random variables.
Ann. Probab. 32 (2004), no. 4, pp. 2884-2907.
- Bobkov, S. G.; Götze, F.
Complement to the paper:
"On the central limit theorem along subsequences of noncorrelated observations"
[Teor. Veroyatnost. i Primenen. 48 (2003), no. 4, 745-765].
Teor. Probab. Appl. 49 (2004), no. 2, pp. 373–375.
- Bobkov, S. G.; Götze, F.
On the central limit theorem along subsequences of noncorrelated observations.
Teor. Veroyatnost. i Primenen. 48 (2003), no. 4, pp. 745-765.
Translation in: Theory Probab. Appl. 48 (2004), no. 4, pp. 604–621.
- Bobkov, S. G; Tetali, P
Modified log-Sobolev inequalities, mixing and hypercontractivity.
Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing,
pp. 287–296 (electronic), ACM, New York, 2003.
- Bobkov, S. G.; Nazarov, F. L.
Large deviations of typical linear functionals on a convex body with unconditional
basis.
Stochastic inequalities and applications, pp. 3–13, Progr. Probab., 56,
Birkhäuser, Basel, 2003.
- Bobkov, S. G.; Nazarov, F. L.
On convex bodies and log-concave probability measures with unconditional basis.
Geometric aspects of functional analysis, pp. 53–69, Lecture Notes in Math., 1807,
Springer, Berlin, 2003.
- Bobkov, S. G.; Koldobsky, A.
On the central limit property of convex bodies.
Geometric aspects of functional analysis, pp. 44–52, Lecture Notes in Math., 1807,
Springer, Berlin, 2003.
- Bobkov, S. G.
Spectral gap and concentration for some spherically symmetric probability measures.
Geometric aspects of functional analysis, pp. 37–43, Lecture Notes in Math., 1807,
Springer, Berlin, 2003.
- Bobkov, S. G.
Concentration of distributions of the weighted sums with Bernoullian coefficients.
Geometric aspects of functional analysis, pp. 27–36, Lecture Notes in Math., 1807,
Springer, Berlin, 2003.
- Bobkov, S. G.
Large deviations via transference plans.
Advances in mathematics research, Vol. 2, pp. 151–175, Adv. Math. Res.,
2, Nova Sci. Publ., Hauppauge, NY, 2003.
- Bobkov, S. G.
On concentration of distributions of random weighted sums.
Ann. Probab. 31 (2003), no. 1, pp. 195–215.
1999-2002
1999-2002
- Bobkov, S. G.
Localization proof of the isoperimetric Bakry-Ledoux inequality and some
applications.
Teor. Veroyatnost. i Primenen. 47 (2002), no. 2, pp. 340--346.
Translation in: Theory Probab. Appl. 47 (2003), no. 2, pp. 308–314.
- Bobkov, S. G.; Gentil, I.; Ledoux, M.
Hypercontractivity of Hamilton-Jacobi equations.
J. Math. Pures Appl. (9) 80 (2001), no. 7, pp. 669–696.
- Bobkov, S. G.; Götze, F.; Houdré, C.
On Gaussian and Bernoulli covariance representations.
Bernoulli 7 (2001), no. 3, pp. 439–451.
- Bobkov, S. G.
Some generalizations of Prokhorov's results on Khinchin-type inequalities for
polynomials.
(Russian) Teor. Veroyatnost. i Primenen. 45 (2000), no. 4, pp. 745-748. Translation in:
Theory Probab. Appl. 45 (2002), no. 4, pp. 644–647.
- Bobkov, S. G.; Ledoux, M.
From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities.
Geom. Funct. Anal. 10 (2000), no. 5, pp. 1028–1052.
- Bobkov, S. G.
Remarks on the growth of Lp-norms of polynomials.
Geometric aspects of functional analysis, pp. 27–35, Lecture Notes in Math.,
1745, Springer, Berlin, 2000.
- Bobkov, S. G.; Houdré, C.
Weak dimension-free concentration of measure.
Bernoulli 6 (2000), no. 4, pp. 621–632.
- Bobkov, S. G.; Houdré, C.; Tetali, P.
λ∞, vertex isoperimetry and concentration.
Combinatorica 20 (2000), no. 2, pp. 153–172.
- Bobkov, S. G.
Isoperimetric and analytic inequalities for log-concave probability measures.
Ann. Probab. 27 (1999), no. 4, pp. 1903–1921.
- Bobkov, S. G.
The size of singular component and shift inequalities.
Ann. Probab. 27 (1999), no. 1, pp. 416–431.
- Bobkov, S. G.; Houdré, C.
A converse Gaussian Poincaré-type inequality for convex functions.
Statist. Probab. Lett. 44 (1999), no. 3, pp. 281–290.
- Bobkov, S. G.; Götze, F.
Discrete isoperimetric and Poincaré-type inequalities.
Probab. Theory Related Fields 114 (1999), no. 2, pp. 245–277.
- Bobkov, S. G.; Götze, F.
Exponential integrability and transportation cost related to logarithmic Sobolev
inequalities.
J. Funct. Anal. 163 (1999), no. 1, pp. 1–28.
1996-1998
1996-1998
- Bobkov, S. G.
Remarks on the Gromov-Milman inequality.
(Russian) Vestnik Syktyvkar Univ., Ser. 1, Mat. Mekh. Inform. No. 3 (1998),
pp. 15–22.
- Bobkov, S. G.; Ledoux, M.
On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures.
J. Funct. Anal. 156 (1998), no. 2, pp. 347–365.
- Bobkov, S. G.; Götze, F.
On moments of polynomials.
Teor. Veroyatnost. i Primenen. 42 (1997), no. 3, pp. 638--640.
Translation in: Theory Probab. Appl. 42 (1997), no. 3, pp. 518–520 (1998).
- Bobkov, S. G.
Isoperimetric problem for uniform enlargement.
Studia Math. 123 (1997), no. 1, pp. 81–95.
- Bobkov, S. G.; Houdré, C.
Isoperimetric constants for product probability measures.
Ann. Probab. 25 (1997), no. 1, pp. 184–205.
- Bobkov, S. G.
An isoperimetric inequality on the discrete cube, and an elementary proof of the
isoperimetric inequality in Gauss space.
Ann. Probab. 25 (1997), no. 1, pp. 206–214.
- Bobkov, S. G.; Ledoux, M.
Poincaré's inequalities and Talagrand's concentration phenomenon for the
exponential distribution.
Probab. Theory Related Fields 107 (1997), no. 3, pp. 383–400.
- Bobkov, S. G.; Houdré, C.
Converse Poincaré-type inequalities for convex functions.
Statist. Probab. Lett. 34 (1997), no. 1, pp. 37–42.
- Bobkov, S. G.
Some extremal properties of the Bernoulli distribution.
(Russian) Teor. Veroyatnost. i Primenen. 41 (1996), no. 4, pp. 877--884.
Translation in: Theory Probab. Appl. 41 (1996), no. 4, pp. 748–755 (1997).
- Bobkov, S. G.; Houdré, C.
Characterization of Gaussian measures in terms of the isoperimetric property of
half-spaces.
(Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov.
(POMI) 228 (1996), Veroyatn. i Stat. 1, pp. 31-38, 356. Translation in:
J. Math. Sci. (New York) 93 (1999), no. 3, pp. 270–275.
Russian version is
here.
- Bobkov, S. G.; Houdré, C.
Variance of Lipschitz functions and an isoperimetric problem for a class of product
measures.
Bernoulli 2 (1996), no. 3, pp. 249–255.
- Bobkov, S. G.
Extremal properties of half-spaces for log-concave distributions.
Ann. Probab. 24 (1996), no. 1, pp. 35–48.
- Bobkov, S. G.
A functional form of the isoperimetric inequality for the Gaussian measure.
J. Funct. Anal. 135 (1996), no. 1, pp. 39–49.
1982-1995
1982-1995
- Bobkov, S. G.
On the Gross and Talagrand inequalities on the discrete cube.
(Russian) Vestn. Syktyvkar. Univ. Ser. 1 Mat. Mekh. Inform. No. 1 (1995),
pp. 12–19.
- Bobkov, S. G.
The Gaussian oscillation on convex sets.
Proceedings of the St. Petersburg Mathematical Society, Vol. IV, pp. 1–17, 1994.
Translation in: Amer. Math. Soc. Transl. Ser. 2, 188, Amer. Math. Soc.,
Providence, RI, 1999.
- Bobkov, S. G.
Isoperimetric inequalities for distributions of exponential type.
Ann. Probab. 22 (1994), no. 2, pp. 978–994.
- Bobkov, S. G.
An isoperimetric problem on the line.
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 216 (1994),
Problemy Teorii Veroyatnost. Raspred. 13, pp. 5-9.
Translation in: J. Math. Sci. (New York) 88 (1998), no. 1, pp. 3–6.
- Bobkov, S. G.
On logarithmically concave measures and their application to random processes
that are linearly generated by independent variables.
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 194 (1992),
Problemy Teorii Veroyatnost. Raspred. 12, pp. 28-29.
Translation in: J. Math. Sci. 75 (1995), no. 5, p. 1889.
- Bobkov, S. G.
Maximum likelihood estimation of a density as an infinite-dimensional Gaussian
shift.
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 177 (1989),
Problemy Teorii Veroyatnost. Raspred. XI, 6-7.
Translation in: J. Soviet Math. 61 (1992), no. 1, pp. 1825–1826.
- Bobkov, S. G.
Upper functions and oscillating Gaussian processes.
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 158 (1987),
Probl. Teor. Veroyatn. Raspred. X, 5-13.
Translation in: J. Soviet Math. 43 (1988), no. 6, pp. 2745–2751.
- Bobkov, S. G.
Variations of random processes with independent increments.
Problems of the theory of probability distributions, VIII. Zap. Nauchn. Sem.
Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 130 (1983), pp. 25–35.
- Bobkov, S. G.
Compact sets of additive measures.
Problems of the theory of probability distributions, VII. Zap. Nauchn. Sem.
Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 119 (1982), pp. 14–18.
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