Spatial-segregation limit for exclusion processes with two components under unbalanced reaction

TL;DR

This paper investigates the limiting behavior of interfaces in a two-component exclusion process with strong competition, where one species is immobile and the other diffuses, revealing three distinct interface regimes.

Contribution

It introduces a novel analysis of interface limits in a two-component exclusion process with unbalanced reaction rates, including cases with immobile species and singular annihilation dynamics.

Findings

Identifies conditions for vanishing, moving, and immovable interfaces.

Derives interface behaviors directly from the interacting particle system.

Utilizes hydrodynamic limit techniques with singular limits for annihilation.

Abstract

We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of two species are given by monomials with distinct exponents. We study limiting behavior of interfaces which appear by such a strong competition. Consequently, three kinds of limiting behavior of interfaces (vanishing, moving and immovable interfaces) are derived directly from our interacting particle system taking advantage of hydrodynamic limit procedure with singular limit for annihilation dynamics.