We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates $$D_A > 0$$ D A > 0 and $$D_B \geqslant 0$$ D B ⩾ 0 , and the interaction is given by mutual annihilation $$A+B \rightarrow \emptyset $$ 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.
Probability Theory and Related Fields – Springer Journals
Published: Apr 1, 2017
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