On the Largest Eigenvalue of Products from the \beta-Laguerre Ensemble

TL;DR

This paper derives the limiting distribution of the largest eigenvalue for products of matrices from the -Laguerre ensemble, showing it follows a Tracy-Widom law with a parameter depending on matrix ratios.

Contribution

It establishes the limiting distribution of the largest eigenvalue for -Laguerre product matrices, extending Tracy-Widom law applicability.

Findings

Largest eigenvalue distribution converges to Tracy-Widom law

Distribution parameter depends on matrix ratio

Results generalize previous single-matrix cases

Abstract

We determine the limiting distribution of the largest eigenvalue of products from the $\beta$-Laguerre ensemble. This limiting distribution is given by a Tracy-Widom law with parameter $\beta_0>0$ depending on the ratio of the parameters of the two matrices involved.