A multi-layer extension of the stochastic heat equation

TL;DR

This paper introduces a multi-layer extension of the stochastic heat equation inspired by solvable directed polymer models, involving non-intersecting Brownian motions to explore complex stochastic systems.

Contribution

It presents a novel multi-layer formulation of the stochastic heat equation based on non-intersecting Brownian motions, expanding the mathematical framework of stochastic PDEs.

Findings

New multi-layer stochastic heat equation model

Connection to solvable directed polymer models

Potential applications in complex stochastic systems

Abstract

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.