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 DA > 0 and DB ≥ 0, and the interaction is given by mutual annihilation A + B → ∅. 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.