The Library
Large deviations analysis for random combinatorial partitions with counter terms
Tools
Adams, Stefan and Dickson, Matthew (2022) Large deviations analysis for random combinatorial partitions with counter terms. Journal of Physics A: Mathematical and Theoretical, 55 (25). 255001. doi:10.1088/1751-8121/ac6f32 ISSN 1751-8113.
|
PDF
WRAP-large-deviations-analysis-random-combinatorial-partitions-counter-terms-Adams-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (1046Kb) | Preview |
Official URL: http://dx.doi.org/10.1088/1751-8121/ac6f32
Abstract
In this paper, we study various models for random combinatorial partitions using large deviation analysis for diverging scale of the reference process. The large deviation rate functions are normalised limiting free energies and the main focus is to study their minimiser for various Gibbsian ensembles with respect to the reference measure which is a probabilistic version of the ideal Bose gas. Scaling limits of similar models have been studied recently (Fatkullin and Slastikov 2018 arXiv:1801.00812v2; Fatkullin and Xue 2021 J. Stat. Phys. 183 22) going back to (Vershik 1996 Func. Anal. Appl. 30 90–105). After studying the reference model, we provide a complete analysis of two mean field models, one of which is well-know (Benfatto et al 2005 J. Math. Phys. 46 033303) and the other one is the cycle mean field model. Both models show critical behaviour despite their rate functions having unique minimiser. The main focus is then a model with negative counter term, the probabilistic version of the so-called Huang–Yang–Luttinger model (van den Berg et al 1988 Commun. Math. Phys. 118 61–85). Criticality in this model is the existence of a critical parameter for which two simultaneous minimiser exists. At criticality an order parameter is introduced as the double limits for the density of cycles with diverging length, and as such it extends recent work in (Adams and Dickson 2021 Ann. Henri Poincaré 22 1535–60).
Item Type: | Journal Article | ||||||
---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Partitions (Mathematics), Probabilities, Large deviations, Combinatorial analysis | ||||||
Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical | ||||||
Publisher: | IOP Publishing Ltd | ||||||
ISSN: | 1751-8113 | ||||||
Official Date: | 1 June 2022 | ||||||
Dates: |
|
||||||
Volume: | 55 | ||||||
Number: | 25 | ||||||
Article Number: | 255001 | ||||||
DOI: | 10.1088/1751-8121/ac6f32 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 6 June 2022 | ||||||
Date of first compliant Open Access: | 7 June 2022 |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year