25 citations · 89 across the 31 of their papers we have counts for
7 papers · 1 filter
Distribution of the minimal distance of random linear codes
Jing Hao, Han Huang, Galyna Livshyts +1
In this paper, we study the distribution of the minimal distance (in the Hamming metric) of a random linear code of dimension in . We provide quantitative estim…
A remark on the smallest singular value of powers of Gaussian matrices
Han Huang, Konstantin Tikhomirov
Let and let be the random matrix with i.i.d. standard real Gaussian entries. We show that there are constants depending only on such tha…
The smallest singular value of inhomogeneous square random matrices
Galyna V. Livshyts, Konstantin Tikhomirov, Roman Vershynin
We show that for an random matrix with independent uniformly anti-concentrated entries, such that , the smallest singular value $…
Hypercontractivity and Lower Deviation Estimates in Normed Spaces
Grigoris Paouris, Konstantin Tikhomirov, Petros Valettas
We consider the problem of estimating small ball probabilities for sub-additive,positively homogeneous functions with respect to th…
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 be a sequence of random symmetric matrices such that…
Estimates for order statistics in terms of quantiles
Alexander E. Litvak, Konstantin Tikhomirov
Let be independent non-negative random variables with cumulative distribution functions , each satisfying certain (rather mild) conditions. W…
Small ball probability for the condition number of random matrices
Alexander E. Litvak, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann
Let be an 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)…