Spectral distribution of large-size Brownian motions on the complex linear group

TL;DR

This paper extends existing methods to analyze the spectral distribution of large-size Brownian motions on the complex linear group, providing insights into their asymptotic behavior.

Contribution

It applies a known approach to describe the large-size limit of the spectral distribution of Brownian motion on the complex linear group.

Findings

Describes the asymptotic spectral distribution for large matrices.

Connects Brownian motion on complex groups with free probability techniques.

Provides a new perspective on spectral analysis of matrix-valued stochastic processes.

Abstract

We show how the approach used in `N. Demni, T. Hmidi. Spectral Distribution of the Free unitary Brownian motion: another approach. Sem. Probab. XLIV. 2012. 191-206.' applies to describe the large-size limit of the marginal distribution of the Brownian motion on the complex linear group.