About

Sergey Bobkov is a professor at the School of Mathematics at the University of Minnesota. His research interests encompass probability theory, analysis, information theory, convex geometry, and discrete mathematics. Specifically, he focuses on high-dimensional distributions, measure concentration phenomena, isoperimetry, transportation, Poincare and logarithmic Sobolev inequalities, entropic inequalities, concentration of information, the Central Limit Theorem, convex bodies and convex measures, localization, graphs, and finite Markov chains. He holds a Dr. Sci. degree in Mathematics and Physics from Saint Petersburg University obtained in 1997, a PhD in Mathematics and Physics from Leningrad University earned in 1988, and a Bachelor's degree in Mathematics from Leningrad University completed in 1983. His academic background and research activities are centered around these areas, contributing to the advancement of mathematical understanding in these fields.

Research topics

• Mathematics
• Applied mathematics
• Statistics
• Mathematical analysis
• Physics
• Geometry
• Statistical physics
• Discrete mathematics
• Combinatorics

Selected publications

• Esscher transform and the central limit theorem

  Journal of Functional Analysis · 2025-04-11

  articleOpen access1st authorCorresponding
  PublisherDOI

• Energy Bounds for Kantorovich Transport Distances with Convex Cost Functions

  ArXiv.org · 2025-12-20

  articleOpen access1st authorCorresponding

  Energy bounds for Kantorovich transport distances are developed for convex cost functions. The main results extend estimates due to M. Ledoux for the Kantorovich distances $W_p$.

  PublisherOA PDF

• Rényi divergences in central limit theorems: Old and new

  Probability Surveys · 2025-01-01

  articleOpen access1st authorCorresponding

  We give an overview of various results and methods related to information-theoretic distances of Rényi type in the light of their applications to the central limit theorem (CLT). The first part (Sections 1–9) is devoted to the total variation and the Kullback-Leibler distance (relative entropy). In the second part (Sections 10–15) we discuss general properties of Rényi and Tsallis divergences of order α>1, and then in the third part (Sections 16–21) we turn to the CLT and non-uniform local limit theorems with respect to these strong distances. In the fourth part (Sections 22–31), we discuss recent results on strictly subgaussian distributions and describe necessary and sufficient conditions which ensure the validity of the CLT with respect to the Rényi divergence of infinite order.

  PublisherOA PDFDOI

• On Subgradients of Convex Functions and Orlicz Pseudo-Norms for Vector-Valued Functions

  arXiv (Cornell University) · 2025-11-28

  preprintOpen access1st authorCorresponding

  We discuss variants of construction of measurable subgradients for multivariate convex functions and the problem of characterization of the $Δ_2$-condition in terms of their directional derivatives. Furthermore we study related basic properties of Luxemburg and Orlicz pseudo-norms for vector-valued functions.

  PublisherOA PDFDOI

• Energy Bounds for Kantorovich Transport Distances with Convex Cost Functions

  arXiv (Cornell University) · 2025-12-20

  preprintOpen access1st authorCorresponding

  Energy bounds for Kantorovich transport distances are developed for convex cost functions. The main results extend estimates due to M. Ledoux for the Kantorovich distances $W_p$.

  PublisherDOI

• Esscher Transform and the Central Limit Theorem

  arXiv (Cornell University) · 2024-07-30 · 1 citations

  preprintOpen access1st authorCorresponding

  The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation for normalized sums of i.i.d. random vectors in terms of the Rényi divergence of infinite order, extending recent one dimensional results.

  PublisherOA PDFDOI

• Correction: Transport Inequalities on Euclidean Spaces for Non-Euclidean Metrics

  Journal of Fourier Analysis and Applications · 2024-09-25 · 1 citations

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Spherical Covariance Representations

  arXiv (Cornell University) · 2024-03-28

  preprintOpen access1st authorCorresponding

  Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concentration inequalities. A detail account is also given in the case of the circle, with a short overview of Höffding's kernels and covariance identities in the class of periodic functions.

  PublisherOA PDFDOI

• On Gilles Pisier’s approach to Gaussian concentration, isoperimetry, and Poincaré-type inequalities

  Electronic Journal of Probability · 2024-01-01

  articleOpen access1st authorCorresponding

  We discuss a natural extension of Gilles Pisier’s approach to the study of measure concentration, isoperimetry, and Poincaré-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measures in the class of rotationally invariant probability distributions on Euclidean spaces, including multidimensional Cauchy measures.

  PublisherOA PDFDOI

• Central Limit Theorem for Rényi Divergence of Infinite Order

  arXiv (Cornell University) · 2024-02-03

  preprintOpen access1st authorCorresponding

  For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities $p_n$ of $Z_n$, this is a strengthened variant of the local limit theorem taking the form $\sup_x (p_n(x) - φ(x))/φ(x) \rightarrow 0$ as $n \rightarrow \infty$.

  PublisherOA PDFDOI

Recent grants

• Geometric and information-theoretic aspects of high-dimensional phenomena

  NSF · $330k · 2011–2015

• Concentration and Related Probabilistic Phenomena in High Dimensions

  NSF · $133k · 2004–2007

• New High Dimensional Phenomena and Applications

  NSF · $200k · 2016–2019

• High-Dimensional Phenomena, Limit Theorems, and Applications

  NSF · $249k · 2019–2022

• Concentration Phenomena In High Dimensions and Applications to Randomized Models

  NSF · $150k · 2007–2010

Frequent coauthors

• Friedrich Götze

  72 shared

• M. Tavani

  National Institute for Astrophysics

  44 shared

• O. V. Serdin

  42 shared

• I. V. Moskalenko

  Stanford University

  41 shared

• P. Picozza

  University of Rome Tor Vergata

  40 shared

• R. Sparvoli

  Istituto Nazionale di Fisica Nucleare, Trento Institute for Fundamental Physics And Applications

  37 shared

• Maxim S. Gorbunov

  IMEC

  36 shared

• A. I. Arkhangelskiy

  Moscow Engineering Physics Institute

  36 shared