Random eigenvalues from a stochastic heat equation

TL;DR

This paper proves the convergence of eigenvalues of a random matrix approximating a stochastic Schrödinger operator derived from a stochastic heat equation, using topological analysis of function spaces.

Contribution

It introduces a novel proof of eigenvalue convergence for operators linked to stochastic heat equations, combining probabilistic and topological methods.

Findings

Eigenvalues of the random matrix converge to those of the stochastic Schrödinger operator.

The proof employs a detailed topological analysis of function spaces.

The approach bridges stochastic PDEs and spectral theory.

Abstract

In this paper we prove the convergence of the eigenvalues of a random matrix that approximates a random Schr\"{o}dinger operator. Originally, such random operator arises from a stochastic heat equation. The proof uses a detailed topological analysis of certain spaces of functions where the operators act.