The KPZ equation and moments of random matrices

TL;DR

This paper establishes a connection between the KPZ equation and the behavior of high powers of random matrices, showing that the logarithm of diagonal elements converges to the KPZ solution.

Contribution

It demonstrates the convergence of the logarithm of diagonal matrix elements of high powers of random matrices to the KPZ equation's solution, linking random matrix theory and stochastic PDEs.

Findings

Logarithm of diagonal matrix elements converges to KPZ solution

Connection between random matrices and stochastic PDEs established

Provides a new perspective on moments of random matrices

Abstract

The logarithm of the diagonal matrix element of a high power of a random matrix converges to the Cole-Hopf solution of the Kardar-Parisi-Zhang equation in the sense of one-point distributions.