Zobrazeno 1 - 10
of 604
pro vyhledávání: '"Götze, F."'
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables whose joint
Externí odkaz:
http://arxiv.org/abs/2308.02693
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, we extend the class $\mathfrak L$ of Newman and propose new sufficient
Externí odkaz:
http://arxiv.org/abs/2308.01749
We consider sparse sample covariance matrices $\frac1{np_n}\mathbf X\mathbf X^*$, where $\mathbf X$ is a sparse matrix of order $n\times m$ with the sparse probability $p_n$. We prove the local Marchenko--Pastur law in some complex domain assuming th
Externí odkaz:
http://arxiv.org/abs/2209.13207
Autor:
Götze, F., Tikhomirov, A.
We derive estimates for the largest and smallest singular values of sparse rectangular $N\times n$ random matrices, assuming $\lim_{N,n\to\infty}\frac nN=y\in(0,1)$. We consider a model with sparsity parameter $p_N$ such that $Np_N\sim \log^{\alpha }
Externí odkaz:
http://arxiv.org/abs/2207.03155
Under Poincar\'e-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 improved concentration inequalities on high-dimensional Euclidean sp
Externí odkaz:
http://arxiv.org/abs/2011.09237
Autor:
Chistyakov, G. P., Götze, F.
Based on the~method of subordinating functions we prove bounds for the minimal error of approximations of $n$-fold convolutions of probability measures by free infinitely divisible probability measures.
Externí odkaz:
http://arxiv.org/abs/2010.06516
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 and R\'enyi/Tsallis relative distances (including Pearson's $\chi^2$).
Externí odkaz:
http://arxiv.org/abs/1906.09156
Under correlation-type conditions, we derive an upper bound of order $(\log n)/n$ for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration i
Externí odkaz:
http://arxiv.org/abs/1906.09063
Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraic conjugate integer coordinates of degree $\leq n$
Externí odkaz:
http://arxiv.org/abs/1704.03542
Autor:
Götze, F.1 (AUTHOR) goetze@math.uni-bielefeld.de, Kabluchko, Z.2 (AUTHOR), Zaporozhets, D.3 (AUTHOR)
Publikováno v:
Journal of Mathematical Sciences. Jul2023, Vol. 273 Issue 5, p738-754. 17p.