Publication: Structure of the Condensed Phase in the Inclusion Process
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Issued Date
2019-01-01
Resource Type
ISSN
15729613
00224715
00224715
Other identifier(s)
2-s2.0-85077040570
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Mahidol University
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SCOPUS
Bibliographic Citation
Journal of Statistical Physics. (2019)
Suggested Citation
Watthanan Jatuviriyapornchai, Paul Chleboun, Stefan Grosskinsky Structure of the Condensed Phase in the Inclusion Process. Journal of Statistical Physics. (2019). doi:10.1007/s10955-019-02451-9 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/51237
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Title
Structure of the Condensed Phase in the Inclusion Process
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Abstract
© 2019, The Author(s). 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.