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Structure of the condensed phase in the inclusion process
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Jatuviriyapornchai, Watthanan , Chleboun, Paul and Grosskinsky, Stefan (2020) Structure of the condensed phase in the inclusion process. Journal of Statistical Physics, 178 . pp. 682-710. doi:10.1007/s10955-019-02451-9
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Official URL: https://doi.org/10.1007/s10955-019-02451-9
Abstract
We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum occupation number. We make use of size-biased sampling to study the structure of the condensed phase, which can extend over more than one lattice site and exhibit an interesting hierarchical structure characterized by the Poisson-Dirichlet distribution. While this approach is established in other areas including population genetics or random permutations, we show that it also provides a powerful tool to analyse homogeneous condensation in stochastic particle systems with stationary product distributions. We discuss the main mechanisms beyond inclusion processes that lead to the interesting structure of the condensed phase, and the connection to other generic particle systems. Our results are exact, and we present Monte-Carlo simulation data and recursive numerics for partition functions to illustrate the main points.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science > Mathematics Faculty of Science > Statistics |
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| Library of Congress Subject Headings (LCSH): | Poisson distribution , Dirichlet problem, Stochastic processes | |||||||||
| Journal or Publication Title: | Journal of Statistical Physics | |||||||||
| Publisher: | Springer New York LLC | |||||||||
| ISSN: | 0022-4715 | |||||||||
| Official Date: | February 2020 | |||||||||
| Dates: |
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| Date of first compliant deposit: | 16 December 2019 | |||||||||
| Volume: | 178 | |||||||||
| Page Range: | pp. 682-710 | |||||||||
| DOI: | 10.1007/s10955-019-02451-9 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Publisher Statement: | This is a post-peer-review, pre-copyedit version of an article published in Journal of Statistical Physics. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]”. | |||||||||
| Access rights to Published version: | Open Access | |||||||||
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