Diffusion-limited annihilating-coalescing systems

Abstract

We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly different jump rates. Upon colliding, like particles coalesce up to some cap and unlike particles annihilate. We describe a phase transition as the initial particle density is varied and provide estimates for the expected occupation time of the root. For the symmetric setting with no cap on coalescence, we prove that the limiting occupation probability of the root is asymptotic to 2/3 the occupation probability for classical coalescing random walk. This addresses an open problem from Stephenson.

arXiv comment16 pages, 4 figures

References in corpus (7)

• The spread of a rumor or infection in a moving population
• Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas
• Stochastic Ballistic Annihilation and Coalescence
• Recurrence and Density Decay for Diffusion-Limited Annihilating Systems
• Mean Field Behavior during the Big Bang Regime for Coalescing Random Walks
• Diffusion-limited annihilating systems and the increasing convex order
• Three-velocity coalescing ballistic annihilation