Recurrence and Density Decay for Diffusion-Limited Annihilating Systems

Abstract

We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition is i.i.d. with finite first moment. We show that this system is site-recurrent, that is, each site is visited infinitely many times. We also generalize a lower bound on the density decay of Bramson and Lebowitz by considering a construction that handles different jump rates.

References in corpus (3)

• Activated Random Walkers: Facts, Conjectures and Challenges
• Absorbing-State Phase Transition for Driven-Dissipative Stochastic Dynamics on $Z$
• Non-equilibrium Phase Transitions: Activated Random Walks at Criticality

Cited by in corpus (5)

• Activated Random Walks on ${\mathbb{Z}}^d$
• Diffusion-limited annihilating systems and the increasing convex order
• Active Phase for Activated Random Walk on Z
• Annihilating branching Brownian motion
• Diffusion-limited annihilating-coalescing systems