Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Anna Lytova"'
Autor:
Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, Alexander E. Litvak, Anna Lytova, Pierre Youssef
Publikováno v:
Journal of the European Mathematical Society. 23:467-501
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7bbe43c176231cdd1474c788bdfcec9
https://doi.org/10.4171/jems/1015
https://doi.org/10.4171/jems/1015
Publikováno v:
Random Matrices: Theory and Applications. 11
Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula:
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43d401fbe7bfc9f55f33c6370d330b1a
https://doi.org/10.1142/s2010326322500307
https://doi.org/10.1142/s2010326322500307
Autor:
Konstantin Tikhomirov, Anna Lytova
Publikováno v:
Probability Theory and Related Fields. 177:465-524
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d244b18c54b9a547dc7de27f18f7f451
https://doi.org/10.1007/s00440-019-00956-8
https://doi.org/10.1007/s00440-019-00956-8
Autor:
Konstantin Tikhomirov, Pierre Youssef, Nicole Tomczak-Jaegermann, Alexander E. Litvak, Anna Lytova
Publikováno v:
Journal of Complexity. 48:103-110
Let d be a (large) integer. Given n ≥ 2 d , let A n be the adjacency matrix of a random directed d -regular graph on n vertices, with the uniform distribution. We show that the rank of A n is at least n − 1 with probability going to one as n grow
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c0a7d30cfbf97159652b9aae2d82b4a
https://doi.org/10.1016/j.jco.2018.05.004
https://doi.org/10.1016/j.jco.2018.05.004
Autor:
Anna Lytova
Publikováno v:
Journal of Theoretical Probability. 31:1024-1057
For $$k,m,n\in {\mathbb {N}}$$ , we consider $$n^k\times n^k$$ random matrices of the form $$\begin{aligned} {\mathcal {M}}_{n,m,k}({\mathbf {y}})=\sum _{\alpha =1}^m\tau _\alpha {Y_\alpha }Y_\alpha ^T,\quad {Y}_\alpha ={\mathbf {y}}_\alpha ^{(1)}\ot
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5231ecdc0797f0237449ddbffcb5db42
https://doi.org/10.1007/s10959-017-0741-9
https://doi.org/10.1007/s10959-017-0741-9
Autor:
Konstantin Tikhomirov, Alexander E. Litvak, Nicole Tomczak-Jaegermann, Pierre Youssef, Anna Lytova
Publikováno v:
Comptes Rendus Mathematique. 354:121-124
Let Dn,dDn,d be the set of all directed d-regular graphs on n vertices. Let G be a graph chosen uniformly at random from Dn,dDn,d and M be its adjacency matrix. We show that M is invertible with probability at least View the MathML source1−Cln3d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::337ac7666f974c3320f45d643c3438b6
https://doi.org/10.1016/j.crma.2015.12.002
https://doi.org/10.1016/j.crma.2015.12.002
Autor:
Pierre Youssef, Nicole Tomczak-Jaegermann, Anna Lytova, Konstantin Tikhomirov, Alexander E. Litvak
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we st
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7644a852fed3419d6efa4d6fee2ef8b3
http://arxiv.org/abs/1801.05575
http://arxiv.org/abs/1801.05575
Autor:
Anna Lytova, Pierre Youssef, Nicole Tomczak-Jaegermann, Konstantin Tikhomirov, Alexander E. Litvak
We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let $$C_1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dfb1b7160a02e6ccbb5783a3e8b3c47f
Autor:
Leonid Pastur, Anna Lytova
Publikováno v:
Metrika. 69:153-172
We consider n × n real symmetric random matrices n−1/2W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n−1ATA with independent entries of m × n matrix A. Assuming first that the 4th cumulant (exce
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::22e9e4e60802f0c77c60df862e1a9951
https://doi.org/10.1007/s00184-008-0212-5
https://doi.org/10.1007/s00184-008-0212-5
Autor:
Anna Lytova, Leonid Pastur
Publikováno v:
Journal of Statistical Physics. 133:871-882
We prove the Law of Large Numbers and the Central Limit Theorem for analogs of U- and V- (von Mises) statistics of eigenvalues of random matrices as their size tends to infinity. We show first that for a certain class of test functions (kernels), det
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::30870e900d4dfed193f0b15cdb88af7e
https://doi.org/10.1007/s10955-008-9644-6
https://doi.org/10.1007/s10955-008-9644-6