K. Tikhomirov

activity

20152021

most citedRandomized coverings of a convex body with its homothetic copies, and illumination

1 citations · 1 across the 6 of their papers we have counts for

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12 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

A remark on the smallest singular value of powers of Gaussian matrices

Han Huang, Konstantin Tikhomirov

Let $n, k \geq 1$ and let $G$ be the $n \times n$ random matrix with i.i.d. standard real Gaussian entries. We show that there are constants $c_{k}, C_{k} > 0$ depending only on $k$ such tha…

math.PR2019

The smallest singular value of inhomogeneous square random matrices

Galyna V. Livshyts, Konstantin Tikhomirov, Roman Vershynin

We show that for an $n \times n$ random matrix $A$ with independent uniformly anti-concentrated entries, such that $E ∣∣ A ∣ ∣_{H S}^{2} \leq K n^{2}$ , the smallest singular value $…

math.PR2019

Outliers in spectrum of sparse Wigner matrices

Konstantin Tikhomirov, Pierre Youssef

In this paper, we study the effect of sparsity on the appearance of outliers in the semi-circular law. Let $(W_{n})_{n = 1}^{\infty}$ be a sequence of random symmetric matrices such that…

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)…