Recurrence and density decay for diffusion-limited annihilating systems

• 成果类型: Article
• 署名作者: Cabezas, M.; Rolla, L. T.; Sidoravicius, V.
• 署名单位: Instituto Nacional de Matematica Pura e Aplicada (IMPA); Pontificia Universidad Catolica de Chile; University of Buenos Aires; New York University; NYU Shanghai; New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0763-3
• 发表日期: 2018
• 页码: 587-615
• 关键词: random-walks; 2-particle reactions; asymptotic-behavior; spatial structure; particle; MODEL; zd

摘要

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 -> empty set. 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.