Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915070526619648 |
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| author | Menshikov, Mikhail Popov, Serguei Wade, Andrew |
| author_facet | Menshikov, Mikhail Popov, Serguei Wade, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates Menshikov, Mikhail Popov, Serguei Wade, Andrew Probability 60K35 (Primary) 60J27, 60K25, 90B22 (Secondary) 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. |
| title | Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates |
| topic | Probability 60K35 (Primary) 60J27, 60K25, 90B22 (Secondary) |
| url | https://arxiv.org/abs/2405.05246 |