F. Götze

activity

19992026

most citedThe circular law for random matrices

112 citations · 441 across the 71 of their papers we have counts for

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Showing 2022 · math.PRShow all

3 papers · 2 filters

math.PR2022

Local Laws for Sparse Sample Covariance Matrices without the truncation condition

F. Götze, A. Tikhomirov, D. Timushev

We consider sparse sample covariance matrices $\frac{1}{n p _{n}} X X^{*}$ , where $X$ is a sparse matrix of order $n \times m$ with the sparse probability $p_{n}$ . We pr…

math.PR2022

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…

math.PR2022

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 $N \times n$ random matrices, assuming $lim_{N, n \to \infty} \frac{n}{N} = y \in (0, 1)$ . We consider a…