Analys- och sannolikhetsseminarium

Abstrakt finns enbart på engelska: We study finite and 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. For finite particle systems, we show that the particle jump rates explicitly determine a unique partition of the system into maximal stable sub-systems and that this partition can be obtained by a linear-time algorithm of elementary steps, as well as by solving a finite non-linear system.

For a semi-infinite particle system, we show that 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.