112 citations · 441 across the 71 of their papers we have counts for
8 papers · 2 filters
Stability of Cramer's Characterization of Normal Laws in Information Distances
S. G. Bobkov, G. P. Chistyakov, F. Götze
Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer's theorem with respect to relative entropy and F…
Arak Inequalities for Concentration Functions and the Littlewood--Offord Problem: a shortened version
Yulia S. Eliseeva, Friedrich Götze, Andrei Yu. Zaitsev
Let be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums $\sum_{k=1}^{n} X_k…
Optimal bounds for convergence of expected spectral distributions to the semi-circular law for the moment ensemble
F. Götze, A. Tikhomirov
This paper extends a previous bound of order of the authors (arXiv:1405.7820[math.PR]), for the rate of convergence in Kolmogorov distance of the expected spectral dist…
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…
Correlation functions of real zeros of random polynomials
Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets
We give an explicit formula for the correlation functions of real zeros of a random polynomial with arbitrary independent continuously distributed coefficients.
Arak Inequalities for Concentration Functions and the Littlewood-Offord Problem
Yulia S. Eliseeva, Friedrich Götze, Andrei Yu. Zaitsev
Let be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums $\sum_{k=1}^{n}a_k X…
Second order concentration on the sphere
S. G. Bobkov, G. P. Chistyakov, F. Götze
Sharpened forms of the concentration of measure phenomenon for classes of functions on the sphere are developed in terms of Hessians of these functions.