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 2015Show all

4 papers · 1 filter

math.PR2015

Adjacency matrices of random digraphs: singularity and anti-concentration

Alexander E. Litvak, Anna Lytova, Konstantin Tikhomirov +2

Let $D_{n, d}$ be the set of all $d$ -regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from $D_{n, d}$ and $M$ be its adjac…

math.PR2015★ 19 cited

On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence

Djalil Chafaï, Konstantin Tikhomirov

Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the larg…

math.PR2015

Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries

Elizaveta Rebrova, Konstantin Tikhomirov

Let $A = (a_{ij})$ be an $n \times n$ random matrix with i.i.d. entries such that $E a_{11} = 0$ and $E a_{11}^{2} = 1$ . We prove that for any $δ > 0$ there is $L > 0$ d…

math.PR2015

Minimax of an n-dimensional Brownian motion

Konstantin Tikhomirov, Pierre Youssef

For some absolute constants $c$ , $n_{0}$ and any $n \geq n_{0}$ , we show that with probability close to one the convex hull of the $n$ -dimensional Brownian motion ${\rm conv}\{BM_n(t):\…