F. Götze

activity

19992026

most citedThe circular law for random matrices

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

collaborators

Showing 2014 · math.PRShow all

8 papers · 2 filters

math.PR2014★ 6 cited

Rate of Convergence of the Expected Spectral Distribution Function to the Marchenko -- Pastur Law

F. Götze, A. N. Tikhomirov

Let $X = (X_{j k})$ denote a $n \times p$ random matrix with entries $X_{j k}$ , which are independent for $1 \leq j \leq n, 1 \leq k \leq p$ . Let $n, p$ tend to infinity such that $\frac…

math.PR2014

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 $X^{(1)}$ and $X^{(2)}$ . Assume that $X_{j k}^{(q)}, 1 \leq j, k \leq n, q = 1, 2,$ are i.i.d.…

math.PR2014★ 4 cited

Asymptotic Spectra of Matrix-Valued Functions of Independent Random Matrices and Free Probability

F. Götze, H. Kösters, A. Tikhomirov

We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several…

math.PR2014★ 2 cited

Asymptotic Expansions in Free Limit Theorems

F. Götze, A. Reshetenko

We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of "influence"…

math.PR2014★ 4 cited

Rate of Convergence of the Empirical Spectral Distribution Function to the Semi-Circular Law

F. Götze, A. N. Tikhomirov

Let $X = (X_{j k})_{j, k = 1}^{n}$ denote a Hermitian random matrix with entries $X_{j k}$ , which are independent for $1 \leq j \leq k \leq n$ . We consider the rate of convergence of the…

math.PR2014★ 1 cited

Optimal Bounds for Convergence of Expected Spectral Distributions to the Semi-Circular Law

F. Götze, A. Tikhomirov

Let $X = (X_{j k})_{j, k = 1}^{n}$ denote a Hermitian random matrix with entries $X_{j k}$ , which are independent for $1 \leq j \leq k \leq n$ . We consider the rate of convergence of the…

math.PR2014★ 10 cited

On one generalization of the elliptic law for random matrices

Friedrich Götze, Alexey Naumov, Alexander Tikhomirov

We consider the products of $m \geq 2$ independent large real random matrices with independent vectors $(X_{j k}^{(q)}, X_{k j}^{(q)})$ of entries. The entries $X_{jk}^{(q)},X_{kj}^{(q)…

math.PR2014

A multiplicative inequality for concentration functions of $n$ -fold convolutions

F. Götze, A. Yu. Zaitsev

We estimate the concentration functions of $n$ -fold convolutions of one-dimensional probability measures. The main result is a supplement to the results of Götze and Zaitsev (1998)…