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

Menshikov, Mikhail V.; Popov, Serguei; Wade, Andrew R.

Abstract

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.

Citation

Menshikov, M. V., Popov, S., & Wade, A. R. (online). Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates. Mathematical Sciences, https://doi.org/10.1007/s00440-024-01357-2

• Journal Article Type: Article
• Acceptance Date: Dec 17, 2024
• Online Publication Date: Jan 13, 2025
• Deposit Date: Dec 18, 2024
• Publicly Available Date: Jan 27, 2025
• Journal: Mathematical Sciences
• Electronic ISSN: 2251-7456
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s00440-024-01357-2
• Public URL: https://durham-repository.worktribe.com/output/3223961