10-1007-s10955-015-1367-x-Accepted-version.pdf (328.98 kB)
Cluster and virial expansions for the multi-species tonks gas
journal contribution
posted on 2023-06-09, 04:40 authored by S JansenWe 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 ?k. 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.
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Publication status
- Published
File Version
- Accepted version
Journal
Journal of Statistical PhysicsISSN
0022-4715Publisher
Springer VerlagExternal DOI
Issue
5Volume
161Page range
1299-1323Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-13First Open Access (FOA) Date
2017-01-13First Compliant Deposit (FCD) Date
2017-01-13Usage metrics
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