26 citations · 134 across the 27 of their papers we have counts for
16 papers · 1 filter
Effective-dimension bounds in the central limit theorem for centered Euclidean balls
Alexey Naumov, Sergey Samsonov, Vladimir Spokoiny +1
We establish a nonasymptotic Gaussian approximation bound over centered Euclidean balls for sums of independent, not necessarily identically distributed, random vectors in \(\mathb…
Sharp Deviations Bounds for Dirichlet Weighted Sums with Application to analysis of Bayesian algorithms
Denis Belomestny, Pierre Menard, Alexey Naumov +2
In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the dens…
Rosenthal-type inequalities for linear statistics of Markov chains
Alain Durmus, Eric Moulines, Alexey Naumov +2
In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independe…
Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains
Alain Durmus, Eric Moulines, Alexey Naumov +1
In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding ineq…
Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables
Sergey G. Bobkov, Alexey A. Naumov, Vladimir V. Ulyanov
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are consi…
Local semicircle law under fourth moment condition
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
We consider a random symmetric matrix with upper triangular entries being independent random variables with mean zero and unit variance. Assuming tha…
Large ball probability, Gaussian comparison and anti-concentration
Friedrich Götze, Alexey Naumov, Vladimir Spokoiny +1
We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bou…
On Local laws for non-Hermitian random matrices and their products
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
The aim of this paper is to prove a local version of the circular law for non-Hermitian random matrices and its generalization to the product of non-Hermitian random matrices under…
On the Local Semicircular Law for Wigner Ensembles
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov +1
We consider a random symmetric matrix with upper triangular entries being i.i.d. random variables with mean zero and unit variance. We additionally s…
Local semicircle law under moment conditions. Part II: Localization and delocalization
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
We consider a random symmetric matrix with upper triangular entries being independent identically distributed random variables with mean zero and uni…
Local semicircle law under moment conditions. Part I: The Stieltjes transform
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
We consider a random symmetric matrix in which the upper triangular entries are independent identically distributed random variables with mean zero a…
Distribution of Linear Statistics of Singular Values of the Product of Random Matrices
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
In this paper we consider the product of two independent random matrices and . Assume that are i.i.d.…
On one generalization of the elliptic law for random matrices
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
We consider the products of independent large real random matrices with independent vectors of entries. The entries $X_{jk}^{(q)},X_{kj}^{(q)…
On minimal singular values of random matrices with correlated entries
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov
Let be a random matrix whose pairs of entries and are correlated and vectors , for , are mutually independent. Assume…
Semicircle Law for a Class of Random Matrices with Dependent Entries
F. Götze, A. Naumov, A. Tikhomirov
In this paper we study ensembles of random symmetric matrices $\X_n = {X_{ij}}_{i,j = 1}^n$ with dependent entries such that $\E X_{ij} = 0$, $\E X_{ij}^2 = σ_{ij}^2$, where $σ_{ij…
Elliptic law for real random matrices
Alexey Naumov
In this paper we consider ensemble of random matrices $\X_n$ with independent identically distributed vectors of entries. Under assumption of finite f…