Pierre Youssef

activity

20152019

collaborators

3 papers

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.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.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):\…