Random partitions in statistical mechanics

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.

38 pages, 3 figures

References in corpus (7)

• Large deviations for random walks under subexponentiality: the big-jump domain
• Spatial random permutations and infinite cycles
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Condensation in zero-range processes on inhomogeneous networks
• The limit shape of random permutations with polynomially growing cycle weights
• Large cycles and a functional central limit theorem for generalized weighted random permutations
• On statistics of permutations chosen from the Ewens distribution

Cited by in corpus (4)

• Condensation and symmetry-breaking in the zero-range process with weak site disorder
• Limit shapes for Gibbs ensembles of partitions
• On Hydrodynamic Limits of Young Diagrams
• On the Asymptotic Distribution of Nucleation Times of Polymerization Processes