112 citations · 441 across the 71 of their papers we have counts for
61 papers · 1 filter
Smallest gaps between zeros of stationary Gaussian processes
Renjie Feng, Friedrich Götze, Dong Yao
In this paper, we study the smallest gaps between successive zeros of nondegenerate smooth stationary centered Gaussian processes on the real line with the assumption that the cova…
Strictly subgaussian probability distributions
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore the class of probability distributions on the real line whose Laplace transform admits a strong upper bound of subgaussian type. Using Hadamard's factorization theorem,…
Local Laws for Sparse Sample Covariance Matrices without the truncation condition
F. Götze, A. Tikhomirov, D. Timushev
We consider sparse sample covariance matrices , where is a sparse matrix of order with the sparse probability . We pr…
Higher order concentration on Stiefel and Grassmann manifolds
Friedrich Götze, Holger Sambale
We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functio…
On the Largest and the Smallest Singular Value of Sparse Rectangular Random Matrices
F. Götze, A. Tikhomirov
We derive estimates for the largest and smallest singular values of sparse rectangular random matrices, assuming . We consider a…
A new bound in the Littlewood--Offord problem
Friedrich Götze, Andrei Yu. Zaitsev
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.
Poincaré Inequalities and Normal Approximation for Weighted Sums
S. G. Bobkov, G. P. Chistyakov, F. Götze
Under Poincaré-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on…
Approximation of free convolutions by free infinitely divisible laws
G. P. Chistyakov, F. Götze
Based on the~method of subordinating functions we prove bounds for the minimal error of approximations of -fold convolutions of probability measures by free infinitely divisible…
Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality
Gernot Akemann, Friedrich Götze, Thorsten Neuschel
We compute the average characteristic polynomial of the hermitised product of real or complex Wigner matrices of size and the average of the characteristic polynomi…
On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem
Friedrich Götze, Andrei Yu. Zaitsev
The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on…
An improved multivariate version of Kolmogorov's second uniform limit theorem
Friedrich Götze, Andrei Yu. Zaitsev, Dmitry Zaporozhets
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be t…
Normal Approximation for Weighted Sums under a Second Order Correlation Condition
S. G. Bobkov, G. P. Chistyakov, F. Götze
Under correlation-type conditions, we derive an upper bound of order for the average Kolmogorov distance between the distributions of weighted sums of dependent summan…
Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy a…
Non-uniform Bounds in the Poisson Approximation with Applications to Informational Distances. I
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson -distance. Th…
Estimates for the closeness of convolutions of probability distributions on convex polyhedra
Friedrich Götze, Andrei Yu. Zaitsev
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson…
Rare events and Poisson point processes
Friedrich Götze, Andrei Yu. Zaitsev
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson law…
Random affine simplexes
Friedrich Götze, Anna Gusakova, Dmitry Zaporozhets
For a fixed consider random vectors with an arbitrary spherically symmetric joint density function. Let be any non-singular…
Higher Order Concentration of Measure
Sergey G. Bobkov, Friedrich Götze, Holger Sambale
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order for any . The bounds are based on $…
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…
New applications of Arak's inequalities to the Littlewood-Offord problem
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_ka_…
Correlations between real and complex zeros of a random polynomial
Friedrich Götze, Denis Koleda, Dmitry Zaporozhets
Consider a random polynomial where are independent real-valued random variables with probability densi…
Rényi divergence and the central limit theorem
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore properties of the and more general Rényi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to…
Second Order Concentration via Logarithmic Sobolev Inequalities
Friedrich Götze, Holger Sambale
We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and secon…