Electronic Journal of Probability

Random partitions in statistical mechanics

Nicholas Ercolani, Sabine Jansen, and Daniel Ueltschi

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Abstract

We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions are invariant for a "chain of Chinese restaurants" stochastic process. We obtain results for the distribution of the size of the largest component.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 82, 37 pp.

Dates
Accepted: 9 September 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065724

Digital Object Identifier
doi:10.1214/EJP.v19-3244

Mathematical Reviews number (MathSciNet)
MR3263639

Zentralblatt MATH identifier
1323.60128

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B05: Classical equilibrium statistical mechanics (general)

Keywords
Spatial random partitions Bose-Einstein condensation (inhomogeneous) zero-range process chain of Chinese restaurants sums of independent random variables heavy-tailed variables infinitely divisible laws

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Ercolani, Nicholas; Jansen, Sabine; Ueltschi, Daniel. Random partitions in statistical mechanics. Electron. J. Probab. 19 (2014), paper no. 82, 37 pp. doi:10.1214/EJP.v19-3244. https://projecteuclid.org/euclid.ejp/1465065724


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