N. Tomczak-Jaegermann

activity

19922019

most citedQuantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles

117 citations · 265 across the 28 of their papers we have counts for

collaborators

35 papers

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)…

math.FA2018

Polylog dimensional subspaces of $ℓ_{\infty}^{N}$

Gideon Schechtman, Nicole Tomczak--Jaegermann

We show that a subspace of of $ℓ_{\infty}^{N}$ of dimension $n > (lo g N lo g lo g N)^{2}$ contains $2$ -isomorphic copies of $ℓ_{\infty}^{k}$ where $k$ tends to infinity with $n/(\log N\l…

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…

math.PR2017★ 12 cited

The smallest singular value of a shifted $d$ -regular random square matrix

Alexander Litvak, Anna Lytova, Konstantin Tikhomirov +2

We derive a lower bound on the smallest singular value of a random $d$ -regular matrix, that is, the adjacency matrix of a random $d$ -regular directed graph. More precisely, let $C_…

Small ball probability for the condition number of random matrices

Polylog dimensional subspaces of ℓ∞N​

Circular law for sparse random regular digraphs

The rank of random regular digraphs of constant degree

Structure of eigenvectors of random regular digraphs

The smallest singular value of a shifted d-regular random square matrix

Polylog dimensional subspaces of $ℓ_{\infty}^{N}$

The smallest singular value of a shifted $d$ -regular random square matrix