A. Litvak

activity

19962026

most citedQuantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles

117 citations · 248 across the 26 of their papers we have counts for

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23 papers · 1 filter

math.PR2020

Singularity of sparse Bernoulli matrices

Alexander E. Litvak, Konstantin E. Tikhomirov

Let $M_{n}$ be an $n \times n$ random matrix with i.i.d. Bernoulli(p) entries. We show that there is a universal constant $C \geq 1$ such that, whenever $p$ and $n$ satisfy $C\log n/n\…

math.PR2019

Estimates for order statistics in terms of quantiles

Alexander E. Litvak, Konstantin Tikhomirov

Let $X_{1}, \dots, X_{n}$ be independent non-negative random variables with cumulative distribution functions $F_{1}, F_{2}, \dots, F_{n}$ , each satisfying certain (rather mild) conditions. W…

math.PR2019

Small ball probability for the condition number of random matrices

Alexander E. Litvak, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann

Let $A$ be an $n \times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)…

math.PR2018

Circular law for sparse random regular digraphs

Alexander Litvak, Anna Lytova, Konstantin Tikhomirov +2

Fix a constant $C \geq 1$ and let $d = d (n)$ satisfy $d \leq ln^{C} n$ for every large integer $n$ . Denote by $A_{n}$ the adjacency matrix of a uniform random directed $d$ -regular graph…

math.PR2018

The rank of random regular digraphs of constant degree

Alexander Litvak, Anna Lytova, Konstantin Tikhomirov +2

Let $d$ be a fixed large integer. For any $n$ larger than $d$ , let $A_{n}$ be the adjacency matrix of the random directed $d$ -regular graph on $n$ vertices, with the uniform distribu…

math.PR2018

Structure of eigenvectors of random regular digraphs

Alexander Litvak, Anna Lytova, Konstantin Tikhomirov +2

Let $d$ and $n$ be integers satisfying $C \leq d \leq exp (c ln n)$ for some universal constants $c, C > 0$ , and let $z \in C$ . Denote by $M$ the adjacency matrix of a r…