K. Tikhomirov

activity

20122026

most citedOn the spectral radius of a random matrix: an upper bound without fourth moment

25 citations · 89 across the 31 of their papers we have counts for

collaborators

Showing 2018Show all

7 papers · 1 filter

math.PR2018

Singularity of random Bernoulli matrices

Konstantin Tikhomirov

For each $n$ , let $M_{n}$ be an $n \times n$ random matrix with independent $\pm 1$ entries. We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an ol…

math.PR2018

On delocalization of eigenvectors of random non-Hermitian matrices

Anna Lytova, Konstantin Tikhomirov

We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n \times n$ random matrix with i.i.d real subgaussian entries of zero…

math.PR2018

The sparse circular law under minimal assumptions

Mark Rudelson, Konstantin Tikhomirov

The circular law asserts that the empirical distribution of eigenvalues of appropriately normalized $n \times n$ matrix with i.i.d. entries converges to the uniform measure on the u…

math.MG2018

On the Banach-Mazur distance to cross-polytope

Konstantin Tikhomirov

Let $n \geq 3$ , and let $B_{1}^{n}$ be the standard $n$ -dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists 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…