# Recurrence and density decay for diffusion-limited annihilating systems

Recurrence and density decay for diffusion-limited annihilating systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Probability Theory and Related Fields Springer Journals

# Recurrence and density decay for diffusion-limited annihilating systems

, Volume 170 (4) – Apr 1, 2017
29 pages

/lp/springer_journal/recurrence-and-density-decay-for-diffusion-limited-annihilating-Q5yjkTHWXA
Publisher
Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Probability Theory and Stochastic Processes; Theoretical, Mathematical and Computational Physics; Quantitative Finance; Mathematical and Computational Biology; Statistics for Business/Economics/Mathematical Finance/Insurance; Operations Research/Decision Theory
ISSN
0178-8051
eISSN
1432-2064
D.O.I.
10.1007/s00440-017-0763-3
Publisher site
See Article on Publisher Site

### 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 $$D_A > 0$$ 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.

### Journal

Probability Theory and Related FieldsSpringer Journals

Published: Apr 1, 2017

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