Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates

• 成果类型: Article
• 署名作者: Menshikov, Mikhail; Popov, Serguei; Wade, Andrew
• 署名单位: Durham University; Universidade do Porto
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-024-01357-2
• 发表日期: 2026-06
• 页码: 73-107
• 关键词: exclusion process; Infinite Jackson network; Interacting Particle Systems; Lattice Atlas model; Asymptotic speeds; Invariant measures; Product-geometric distribution; zero-range process; models; condensation

摘要

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. Under appropriate hypotheses on the jump rates (uniformly bounded rates is sufficient) and started from an initial condition that is a finite perturbation of the close-packed configuration, we give conditions under which the particles evolve as a single, semi-infinite stable cloud. More precisely, we show that inter-particle separations converge to a product-geometric stationary distribution, and that the location of every particle obeys a strong law of large numbers with the same characteristic speed.