A traffic approach for profiled Pennington-Worah matrices

TL;DR

This paper analyzes large random matrices derived from Pennington and Worah's models, revealing new insights into their spectral properties and a linear plus chaos phenomenon through a traffic approach.

Contribution

It introduces a traffic-based decomposition for these matrices, extending previous work and providing a new interpretation of their spectral behavior.

Findings

Decomposition of Pennington-Worah matrices into asymptotically traffic-equivalent components

Identification of a linear plus chaos phenomenon in the spectral analysis

Extension of previous results to matrices with entry-wise varying variance

Abstract

We study macroscopic observables of large random matrices introduced by Pennington and Worah, defined by applying entry wise a non linear function on a product of matrices with independent entries. We allow the variance of the entries of the matrices to vary from entry to entry. We complement P\'ech\'e perspective from [Electron. Commun. Probab. 24 (2019)] showing a decomposition of these matrices whose and traffic asymptotic traffic-equivalent for their ingredients, when the activation function belongs to the space of odd polynomials. This give a new interpretation of the linear plus chaos phenomenon observed for these matrices.