Sumit Mukherjee

I did my Ph.D at Stanford University, under the supervision of Prof. Persi Diaconis. In Fall 2014, I joined the Department of Statistics at Columbia University as an Assistant Professor. Starting from Fall 2020, I am an Associate Professor at Columbia. My email id is sm3949@columbia.edu. Here is a link to my CV, and my Google Scholar page .

My research interests lie in the intersection of Mathematical Statistics, Probability, and Combinatorics. One of my main interests is to develop statistical theory and methods for inference with dependent combinatorial data, such as Ising models and more general discrete Markov random fields, Mallows models on ranking, and exponential random graph models (ERGMs). In another direction I study persistence (above a level line) for "approximately" stationary Gaussian processes. I also study limiting distributions of random multilinear/tensor forms arising from graph coloring problems. I gratefully acknowledge NSF (DMS-2113414, DMS-1712037) for partially supporting my research.

Preprints

Random Permutations

S. Mukherjee, Estimation in exponential families on permutations, Supplement, Annals of Statistics, 44(2):853-875, 2016.

S. Mukherjee, Fixed points and cycle structure of random permutations, Electronic Journal of Probability, 21:1-18, 2016.

B. B. Bhattacharya and S. Mukherjee, Degree Sequence of Random Permutation Graphs, Annals of Applied Probability, 27(1):439-484, 2017.

J. Borga, S. Das, S. Mukherjee and P. Winkler, Large deviation principle for random permutations , to appear in International Mathematics Research Notices.

S. Mukherjee and D. Tagami, Inference on a class of exponential families on permutations , Submitted.

Mean field Gibbs measures

A. Basak and S. Mukherjee, Universality of the mean-field for the Potts model, Probability Theory and Related Fields, 168(3):557-600, 2017.

B. B. Bhattacharya and S. Mukherjee, Inference in Ising Models, Bernoulli , 24(1):493-525, 2018.

R. Mukherjee, S. Mukherjee and M. Yuan, Global testing against sparse alternatives under Ising models, Supplement, Annals of Statistics, 46(5):2062-2093, 2018.

P. Ghosal and S. Mukherjee, Joint estimation of parameters in Ising model, Annals of Statistics, 48(2):785-810, 2020.

S. Mukherjee and S. Sen, Variational Inference in high-dimensional linear regression, Journal of Machine Learning Research, 23(304):1-56, 2022.

N. Deb and S. Mukherjee, Fluctuations in Mean-Field Ising models, Annals of Applied Probability, 33(3):1961-2003, 2023.

Y. Xu and S. Mukherjee, Ising Models on Dense Regular Graphs, Annals of Statistics, 51(3):1183-1206, 2023.

N. Deb, R. Mukherjee, S. Mukherjee and M. Yuan, Detecting Structured Signals in Ising Models, to appear in Annals of Applied Probability.

D. Lacker, S. Mukherjee and L.C. Yeung, Mean field approximations via log-concavity , to appear in International Mathematics Research Notices.

C.C. Margossian and S. Mukherjee, Simulating Ising and Potts models at critical and cold temperatures using auxiliary Gaussian variables , Submitted.

S. Bhattacharya, N. Deb and S. Mukherjee, LDP for Inhomogeneous U-Statistics , Submitted.

S. Bhattacharya, N. Deb and S. Mukherjee, Gibbs Measures with Multilinear Forms , Submitted.

S. Mukherjee, B. Sen and S. Sen, A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression , Submitted.

Persistence of Gaussian processes

A. Dembo and S. Mukherjee, No zero-crossings for random polynomials and the heat equation, Annals of Probabability, 43(1):85-118, 2015.

A. Dembo and S. Mukherjee, Persistence of Gaussian processes: non-summable correlations, Probability Theory and Related Fields, 169(3):1007-1039, 2017.

F. Aurzada, S. Mukherjee and O. Zeitouni, Persistence exponents in Markov chains, Annales de l’Institut Henri Poincaré , 57(3):1411-1441, 2021.

F. Aurzada and S. Mukherjee, Persistence probabilities of weighted sums of stationary Gaussian sequences, Stochastic Processes and their Applications , 159:286-319, 2023.

N. D. Feldheim, O. N. Feldheim and S. Mukherjee, Persistence and Ball Exponents for Gaussian Stationary Processes, Submitted.

Limit distributions for multilinear forms

B. B. Bhattacharya, P. Diaconis and S. Mukherjee, Universal Poisson and Normal Limit Theorems in Graph Coloring Problems With Connections to Extremal Combinatorics, Annals of Applied Probability, 27(1):337-394, 2017.

B.B. Bhattacharya and S. Mukherjee, Limit Theorems for Monochromatic Stars, Random Structures and Algorithms, 55(4):831-853, 2019.

B.B. Bhattacharya and S. Mukherjee, Monochromatic Subgraphs in Randomly Colored Graphons, European Journal of Combinatorics, 81:328-353, 2019.

B.B. Bhattacharya, S. Mukherjee and S. Mukherjee, Birthday Paradox, Monochromatic Subgraphs, and the Second Moment Phenomenon, SIAM Journal of Discrete Mathematics, 34(1):794-824, 2020.

B.B. Bhattacharya, S. Mukherjee and S. Mukherjee, Asymptotic Distribution of Bernoulli Quadratic Forms, Annals of Applied Probability, 31(4):1548-1597, 2021.

B.B. Bhattacharya, S. Das, S. Mukherjee and S. Mukherjee, Asymptotic Distribution of Random Quadratic Forms , Submitted.

Statistics on Networks

R. Mukherjee, S. Mukherjee and S. Sen, Detection thresholds for the beta model in sparse graphs, Supplement, Annals of Statistics, 46(3):1288-1317, 2018.

S. Mukherjee, Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics, Bernoulli, 26(2):1016-1043, 2020.

B.B. Bhattacharya, S. Das and S. Mukherjee, Motif Estimation via Subgraph Sampling: The Fourth Moment Phenomenon , Annals of Statistics., 50(2): 987-1011, 2022.

S. Mukherjee and Y. Xu, Statistics of the two-star ERGM, Bernoulli, 29(1):24-51, 2023.

Y. Xu and S. Mukherjee, Signal Detection in Degree Corrected ERGMs , to appear in Bernoulli.

Miscellanous

B. B. Bhattacharya and S. Mukherjee, Exact and Asymptotic Results on Coarse Ricci Curvature of Graphs, Discrete Mathematics, 338(1):23-42, 2015.

S. Chatterjee and S. Mukherjee, On Estimation in Tournaments and Graphs under Monotonicity Constraints, IEEE Transactions of Information Theory , 65(6):3525-3539, 2019.