Spectrum of deformed random matrices and free probability
M Capitaine, C Donati-Martin (LM-Versailles)
TL;DR
This paper explores how free probability theory helps understand the spectral properties of deformed random matrices, unifying various asymptotic phenomena like spectral measures, eigenvalue localization, and eigenvector behavior.
Contribution
It provides a unified framework using free probability to analyze spectral properties and asymptotic behaviors of deformed random matrices.
Findings
Spectral measures are characterized using free probability techniques.
Localization and fluctuations of extremal eigenvalues are described.
Eigenvector behavior is analyzed within the free probability framework.
Abstract
The aim of this paper is to show how free probability theory sheds light on spectral properties of deformed matricial models and provides a unified understanding of various asymptotic phenomena such as spectral measure description, localization and fluctuations of extremal eigenvalues, eigenvectors behaviour.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Spectral Theory in Mathematical Physics