Konstantin Tikhomirov

About

Konstantin Tikhomirov works in discrete probability, combinatorics, and convex geometry, with applications to data analysis. His research focuses on the properties of random matrices, spectral theory, and geometric aspects of functional analysis, contributing to understanding invertibility, singular values, and eigenvector delocalization of random matrices, as well as the geometry of convex bodies and polytopes. He has made significant contributions to the study of the smallest singular value of random matrices, the spectral radius of random matrices, and the behavior of eigenvectors in non-Hermitian matrices. His work also includes investigations into the structure of eigenvectors of random regular digraphs, the distribution of minimal distances in random linear codes, and the properties of convex hulls of random points. Tikhomirov's research extends to the analysis of random graph models, the spectral gap of regular graphs, and the geometric and probabilistic properties of high-dimensional spaces, establishing foundational results and new techniques in these areas.

Research topics

• Mathematics
• Combinatorics
• Discrete mathematics
• Pure mathematics
• Applied mathematics

Selected publications

• On Bounded Degree Graphs with Large Size-Ramsey Numbers

  COMBINATORICA · 2023-08-21 · 5 citations

  article1st authorCorresponding
  PublisherDOI

• On dimension-dependent concentration for convex Lipschitz functions in product spaces

  Electronic Journal of Probability · 2023-01-01 · 4 citations

  articleOpen accessSenior author

  Let n≥1, K>0, and let X=(X1,X2,…,Xn) be a random vector in Rn with independent K–subgaussian components. We show that for every 1–Lipschitz convex function f in Rn (the Lipschitzness with respect to the Euclidean metric), ∀t>0, max(P{f(X)−Medf(X)≥t},P{f(X)−Medf(X)≤−t})≤exp(−ct2 K2log(2+K2n t2)), where c>0 is a universal constant. The estimates are optimal in the sense that for every n≥C˜ and t>0 there exist a product probability distribution X in Rn with K–subgaussian components, and a 1–Lipschi…

  PublisherOA PDFDOI

• Upgrading MLSI to LSI for reversible Markov chains

  Journal of Functional Analysis · 2023-06-28 · 4 citations

  articleOpen access
  PublisherOA PDFDOI

• Average-case analysis of the Gaussian elimination with partial pivoting

  Probability Theory and Related Fields · 2024-04-22 · 2 citations

  articleOpen accessSenior authorCorresponding

  Abstract The Gaussian elimination with partial pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical evidence strongly suggests that for a typical square coefficient matrix, GEPP is numerically stable. We obtain a (partial) theoretical justification of this phenomenon by showing that, given the random $$n\times n$$ <mml:math xmlns:mml="http://www.w3.org/1…

  PublisherOA PDFDOI

• A remark on the Ramsey number of the hypercube

  European Journal of Combinatorics · 2024-03-25 · 1 citations

  article1st authorCorresponding
  PublisherDOI

Recent grants

• Random Matrices and Functional Inequalities on Spaces of Graphs

  NSF · $261k · 2021–2023

Frequent coauthors

• Pierre Youssef

  New York University Abu Dhabi

  61 shared

• Alexander E. Litvak

  University of Alberta

  24 shared

• Anna Lytova

  20 shared

• Nicole Tomczak-Jaegermann

  University of Alberta

  16 shared

• С. В. Асташкин

  Moscow Center For Continuous Mathematical Education

  12 shared

• Galyna V. Livshyts

  12 shared

• Mark Rudelson

  University of Michigan–Ann Arbor

  9 shared

• Han Huang

  8 shared

Education

• Ph.D., Canada

  University of Alberta

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