Bogachev, LV orcid.org/0000-0002-2365-2621 and Yakubovich, YV (2020) Limit Shape of Minimal Difference Partitions and Fractional Statistics. Communications in Mathematical Physics, 373 (3). pp. 1085-1131. ISSN 0010-3616
Abstract
The class of minimal difference partitionsMDP(q) (with gap q) is defined by the condition that successive parts in an integer partition differ from one another by at least q≥0. In a recent series of papers by A. Comtet and collaborators, the MDP(q) ensemble with uniform measure was interpreted as a combinatorial model for quantum systems with fractional statistics, that is, interpolating between the classical Bose–Einstein (q=0) and Fermi–Dirac (q=1) cases. This was done by formally allowing values q∈(0,1) using an analytic continuation of the limit shape of the corresponding Young diagrams calculated for integer q. To justify this “replica-trick”, we introduce a more general model based on a variable MDP-type condition encoded by an integer sequence q=(qi), whereby the (limiting) gap q is naturally interpreted as the Cesàro mean of q. In this model, we find the family of limit shapes parameterized by q∈[0,∞) confirming the earlier answer, and also obtain the asymptotics of the number of parts.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019, The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | integer partitions; minimal difference partitions; Young diagrams; limit shape; fractional statistics; equivalence of ensembles |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Jul 2019 10:36 |
Last Modified: | 25 Jun 2023 21:55 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00220-019-03513-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:148891 |
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