A Spectral Dominance Approach to Large Random Matrices - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2021

A Spectral Dominance Approach to Large Random Matrices

Résumé

This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure can be determined as the derivative of the unique viscosity solution of a partial integro-differential equation. This also allows to make general and "short" proofs for the convergence problem. We treat the cases of Dyson Brownian motions, Wishart processes and present a general class of models for which this characterization holds.
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Dates et versions

hal-03228966 , version 2 (18-05-2021)
hal-03228966 , version 1 (12-10-2023)

Identifiants

Citer

Charles Bertucci, Mérouane Debbah, Jean-Michel Lasry, Pierre-Louis Lions. A Spectral Dominance Approach to Large Random Matrices. 2023. ⟨hal-03228966v1⟩
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