LDP for the largest eigenvalue of Kronecker random matrices

TL;DR

This paper establishes a large deviations principle for the largest eigenvalue of Gaussian Kronecker matrices, which are formed by tensor products of independent Gaussian matrices, in the high-dimensional limit.

Contribution

It provides the first large deviations result for the largest eigenvalue of Gaussian Kronecker matrices in the asymptotic regime.

Findings

Large deviations principle proven for the largest eigenvalue

Results applicable in high-dimensional tensor product regimes

Advances understanding of spectral properties of Kronecker matrices

Abstract

We prove a large deviations principle for the largest eigenvalue of Gaussian Kronecker matrices, namely matrices defined as the sum of tensors of independent Gaussian matrices in the regime where the dimension of the Gaussian matrices goes to infinity.