Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Konstantin Tikhomirov"'
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
Autor:
Konstantin Tikhomirov
Publikováno v:
Random Structures & Algorithms. 57:526-562
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8a558241a4a5a4d84002f621c3b64869
https://doi.org/10.1002/rsa.20920
https://doi.org/10.1002/rsa.20920
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
This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi graphs marg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db48a949526d9bc4b5cd8c39e86f149a
http://arxiv.org/abs/2110.05000
http://arxiv.org/abs/2110.05000
Publikováno v:
Discrete & Computational Geometry. 63:209-228
It was conjectured by Levi, Hadwiger, Gohberg and Markus that the boundary of any convex body in $${\mathbb R}^n$$ can be illuminated by at most $$2^n$$ light sources, and, moreover, $$2^n-1$$ light sources suffice unless the body is a parallelotope.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::02c1eff5a981c5dd86e4ad8642015948
https://doi.org/10.1007/s00454-019-00115-9
https://doi.org/10.1007/s00454-019-00115-9
Autor:
Konstantin Tikhomirov, Mark Rudelson
Publikováno v:
Geometric and Functional Analysis. 29:561-637
The circular law asserts that the empirical distribution of eigenvalues of appropriately normalized $${n \times n}$$ matrix with i.i.d. entries converges to the uniform measure on the unit disc as the dimension n grows to infinity. Consider an $${n \
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b4f1332f53ab28a1771a60d9bdf8082
https://doi.org/10.1007/s00039-019-00492-6
https://doi.org/10.1007/s00039-019-00492-6
Autor:
Konstantin Tikhomirov
Publikováno v:
Advances in Mathematics. 345:598-617
Let n ≥ 3 , and let B 1 n be the standard n-dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists a symmetric convex body G m in R n such that the Banach–Mazur distance d B
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::28ec05c6dc45d669b8f821e5efc127ab
https://doi.org/10.1016/j.aim.2019.01.013
https://doi.org/10.1016/j.aim.2019.01.013
Publikováno v:
ISIT
In this paper, we study the distribution of the minimum distance (in the Hamming metric) of a random linear code of dimension k in $\mathbb{F}_q^n$. We provide quantitative estimates showing that the distribution function of the minimum distance is c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e55861be5cbfcd80ec8bfb1fb49e2e25
https://doi.org/10.1109/isit44484.2020.9173937
https://doi.org/10.1109/isit44484.2020.9173937
Autor:
Konstantin Tikhomirov
Publikováno v:
Annals of Mathematics. 191
For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries. We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an old problem. Some generalizations are considered.
Rearranged auxili
Rearranged auxili
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fef09a57c778cc3dbd3fb893e7006ac3
https://doi.org/10.4007/annals.2020.191.2.6
https://doi.org/10.4007/annals.2020.191.2.6
Autor:
Han Huang, Konstantin Tikhomirov
Publikováno v:
Electron. Commun. Probab.
Let $n,k\geq 1$ and let $G$ be the $n\times n$ random matrix with i.i.d. standard real Gaussian entries. We show that there are constants $c_k,C_k>0$ depending only on $k$ such that the smallest singular value of $G^k$ satisfies $$ c_k\,t\leq {\mathb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f932ccd6ae07292b32e148d84842174
https://doi.org/10.1214/20-ecp285
https://doi.org/10.1214/20-ecp285