Cluster and virial expansions for the multi-species tonks gas

Jansen, S (2015) Cluster and virial expansions for the multi-species tonks gas. Journal of Statistical Physics, 161 (5). pp. 1299-1323. ISSN 0022-4715

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Abstract

We consider a mixture of non-overlapping rods of different lengths ℓk moving in R or Z. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities zk and the densities ρk. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-overlapping rods and labelled rooted trees. We also prove that for certain choices of the activities, the system can undergo a condensation transition akin to that of the zero-range process. The key tool is a fixed point equation for the pressure.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 13 Jan 2017 15:07
Last Modified: 06 Mar 2017 19:21
URI: http://sro.sussex.ac.uk/id/eprint/66145

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