Approach to equilibrium for Markovian infinite particle systems with exclusion interaction
AuthorKeisling, John Davis, 1969-
AdvisorFaris, William G.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractThe N-exclusion process is an interacting particle system that generalizes the simple exclusion process by allowing up to N particles at each site. In this work, we define the jump rates to be 1 if any particles are present and 0 if not, and we consider the infinite-volume limit of this process in arbitrary dimension. Assuming symmetry and translation invariance of the underlying Markov chain, we show that the extremal translation-invariant stationary measures are product measures, one for each given "density" of particles. With the further assumption of irreducibility, we generalize a coupling argument of Liggett to show that every translation-invariant measure converges to a mixture of these product measures.
Degree ProgramGraduate College