Home Page for Arnab Sen

I am an associate professor of Mathemetics at University of Minnesota. I was a postdoctoral fellow in Statistical Laboratory, University of Cambridge. My host was Prof. Nathanaël Berestycki. I finished my PhD in 2010 from the Department of Statistics at UC Berkeley. My advisors were Prof. Steven N. Evans and Prof. Elchanan Mossel. Research Interests: I have a broad interest in discrete probability. I am particularly interested in various models in statistical physics, such as spin glasses, along with random graphs, random matrices, and random polynomials.

Research

• On the replica symmetric solution in general diluted spin glasses. Joint with Ratul Biswas and Wei-Kuo Chen. Preprint, (2024).
  
  
• Joint parameter estimations for spin glasses. Joint with Wei-Kuo Chen and Qiang Wu. Preprint, (2024).
  
  
• Disorder chaos in short-range, diluted, and Levy spin glasses. Joint with Wei-Kuo Chen and Heejune Kim. Preprint, (2024).
  
  
• Minimal spanning arborescence. Joint with Gourab Ray. Preprint, (2024).
  
  
• Some rigorous results on the Levy spin glass model. Joint with Wei-Kuo Chen and Heejune Kim. Preprint, (2023).
  
  
• Limiting eigenvalue distribution of heavy-tailed Toeplitz matrices. Joint with Rtaul Biswas. To appear in Annales de l'Institut Henri Poincarè (B), (2022).
  
  
• Central limit theorem in disordered monomer-dimer model. Joint with Wai-Kit Lam. To appear in Random Structures and Algorithms, (2022).
  
  
• Free energy of a diluted spin glass model with quadratic Hamiltonian. Joint with Ratul Biswas and Wei-Kuo Chen. Annals of Probability, 51(1), 359-395 (2023).
  
  
• On ℓ_p-Gaussian-Grothendieck problem. Joint with Wei-Kuo Chen. International Mathematics Research Notices, 23(3), 2344-2428 (2023).
  
  
• Scaling limit of soliton lengths in a multicolor box-ball system. Joint with Joel Lewis, Hanbaek Lyu, and Pavlo Pylyavskyy. To appear in Forum of Mathematics, Sigma, (2019).
  
  
• Zero-temperature Glauber dynamics on the 3-regular tree and the median process. Joint with Michael Damron. Probability Theory and Related Fields, 178, 25-68 (2020).
  
  
• Double roots of random polynomials with integer coefficients . Joint with Ohad N. Feldheim. Electronic Journal in Probability, 22, 1-23 (2017).
  
  
• Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p-spin models . Joint with Wei-Kuo Chen. Communications in Mathematical Physics 350, 129-173 (2017).
  
  
• Mean quantum percolation . Joint with Charles Bordenave and Bàlint Viràg. Journal of European Mathematical Society, 19(12), 3679-3707 (2017).
  
  
• Double roots of random Littlewood polynomials. Joint with Ron Peled and Ofer Zeitouni. Israel J. Math, 216(1), 55-77 (2016).
  
  
• Juntas in the ℓ¹-grid and Lipschitz maps between discrete tori. Joint with Itai Benjamini, David Ellis, Ehud Friedgut and Nathan Keller. Random Structures and Algorithms, 49(2), 253-279 (2016).
  
  
• Extinction Window of Mean Field Branching Annihilating Random Walk . Joint with Idan Perl and Ariel Yadin. Annals of Appiled Probability, 25(6), 3139-3161 (2015).
  
  
• Coalescing Brownian flows: a new approach. Joint with Nathanaël Berestycki, Christophe Garban. Annals of Probability, 43(6), 3177-3215 (2015).
  
  
• On Testing Independence and Goodness-of-fit in Linear Models. Joint with Bodhisattva Sen. Biometrika , 101(4), 927-942 (2014).
  
  
• Geometric Influences II: Correlation Inequalities and Noise Sensitivity. Joint with Nathan Keller and Elchanan Mossel. Annales de l'Institut Henri Poincarè (B), 50(4), 1121-1139 (2014).
  
  
• Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix. Joint with Bàlint Viràg. Electron Commun Probab, 16, 706-711 (2011).
  
  
• The top eigenvalue of the random Toeplitz matrix and the Sine kernel. Joint with Bàlint Viràg. Annals of Probability, 41(6), 4050-4079 (2013).
  
  
• On reverse hypercontractivity. Joint with Elchanan Mossel and Krzysztof Oleszkiewicz. Geometric and Functional Analysis 23(3), 1062-1097 (2013).
  
  
• Stochastic population growth in spatially heterogeneous environments. Joint with Steve Evans, Peter Ralph, and Sebastian Schreiber. J. of Math. Bio. 66(3), 423-476 (2013).
  
  
• Coalescing systems of non-Brownian particles . Joint with Steve Evans and Ben Morris. Probability Theory and Related Fields 156 (1-2), 307-342 (2013).
  
  
• Geometric Influences. Joint with Nathan Keller and Elchanan Mossel. Annals of Probability 40(3), 1135-1166 (2012).
  
  
• Spectra of large random trees. Joint with Shankar Bhamidi and Steven N. Evans. Journal of Theoretical Probab, 25(3), 613-654 (2012).
  
  
• Limiting Spectral distribution of random k-circulants. Joint with Arup Bose and Joydip Mitra. Journal of Theoretical Probab, 25(3), 771-797 (2012).
  
  
• Scaling limits for width two partially ordered sets: The Incomparability Window. With Nayantara Bhatnagar, Nick Crawford and Elchanan Mossel. Order 289-311 (2013).
  
  
• Branching Process approach for 2-SAT thresholds. Joint with Elchanan Mossel. Journal of Applied Probab. 47(3), 796-810 (2010).
  
  
• Limiting spectral distribution of XX' matrices. Joint with Arup Bose and Sreela Gangopadhyay. Annales de l'Institut Henri Poincarè (B), 46(3), 677-707 (2010).
  
  
• Another look at the moment method for large dimensional random matrices. Joint with Arup Bose. Electronic Journal In Probability, 13, 588-628 (2008).
  
  
• On asymptotic properties of the rank of a special random adjacency matrix. Joint with Arup Bose. Electronic Communications In Probability, 13, 200-205 (2007).
  
  
• Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices. Joint with Arup Bose. Electronic Communications In Probability, 13, 21-27 (2007).
  
  

Past Teaching

UMN
Fall 2019 Math 8660: Random Matrix Theory
Spring 2019
Theory of Probability Including Measure Theory II
Fall 2016, 2017
Math 5652: Introduction to Stochastic Processes
Spring 2016
Theory of Probability Including Measure Theory II
Math 5652: Introduction to Stochastic Processes
Fall 2015, 2018
Theory of Probability Including Measure Theory I
Fall 2014
Math 2263: Multivariable Calculus.
Spring 2014
Math 5651: Basic Theory of Probability and Statistics.
Math 8660: Random Matrix Theory. Fall 2012
Math 5651: Basic Theory of Probability and Statistics.