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pro vyhledávání: '"Lytova, Anna"'
Given $n,m\in \mathbb{N}$, we study two classes of large random matrices of the form $$ \mathcal{L}_n =\sum_{\alpha=1}^m\xi_\alpha \mathbf{y}_\alpha \mathbf{y}_\alpha ^T\quad\text{and}\quad \mathcal{A}_n =\sum_{\alpha =1}^m\xi_\alpha (\mathbf{y}_\alp
Externí odkaz:
http://arxiv.org/abs/2103.03204
Autor:
Lytova, Anna, Tikhomirov, Konstantin
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n\times n$ random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $1-e^{-
Externí odkaz:
http://arxiv.org/abs/1810.01590
Autor:
Litvak, Alexander, Lytova, Anna, Tikhomirov, Konstantin, Tomczak-Jaegermann, Nicole, Youssef, Pierre
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 on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the
Externí odkaz:
http://arxiv.org/abs/1801.05576
Autor:
Litvak, Alexander, Lytova, Anna, Tikhomirov, Konstantin, Tomczak-Jaegermann, Nicole, Youssef, Pierre
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we st
Externí odkaz:
http://arxiv.org/abs/1801.05575
Autor:
Litvak, Alexander, Lytova, Anna, Tikhomirov, Konstantin, Tomczak-Jaegermann, Nicole, Youssef, Pierre
Publikováno v:
Journal of Complexity Volume 48, October 2018, Pages 103-110
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 distribution. We show that $A_n$ has rank at least $n-1$ with probability goin
Externí odkaz:
http://arxiv.org/abs/1801.05577
Autor:
Litvak, Alexander, Lytova, Anna, Tikhomirov, Konstantin, Tomczak-Jaegermann, Nicole, Youssef, Pierre
Publikováno v:
Probability Theory and Related Fields, 2018
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_1
Externí odkaz:
http://arxiv.org/abs/1707.02635
Autor:
Lytova, Anna, Tikhomirov, Konstantin
Let $n$ be a large integer, and let $G$ be the standard Gaussian vector in $R^n$. Paouris, Valettas and Zinn (2015) showed that for all $p\in[1,c\log n]$, the variance of the $\ell_p^n$--norm of $G$ is equivalent, up to a constant multiple, to $\frac
Externí odkaz:
http://arxiv.org/abs/1705.05052
Autor:
Lytova, Anna
For $k,m,n\in \mathbb{N}$, we consider $n^k\times n^k$ random matrices of the form $$ \mathcal{M}_{n,m,k}(\mathbf{y})=\sum_{\alpha=1}^m\tau_\alpha {Y_\alpha}Y_\alpha^T,\quad Y_\alpha=\mathbf{y}_\alpha^{(1)}\otimes...\otimes\mathbf{y}_\alpha^{(k)}, $$
Externí odkaz:
http://arxiv.org/abs/1602.08613
Autor:
Litvak, Alexander E., Lytova, Anna, Tikhomirov, Konstantin, Tomczak-Jaegermann, Nicole, Youssef, Pierre
Publikováno v:
J. of Math. Analysis and Appl., 445 (2017), 1447--1491
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least
Externí odkaz:
http://arxiv.org/abs/1511.00113
Autor:
Lytova, Anna, Pastur, Leonid
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions under whic
Externí odkaz:
http://arxiv.org/abs/1503.04353