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The geometric Burge correspondence and the partition function of polymer replicas
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Bisi, Elia, O’Connell, Neil and Zygouras, Nikos (2021) The geometric Burge correspondence and the partition function of polymer replicas. Selecta Mathematica, New Series, 27 . 100. doi:10.1007/s00029-021-00712-8 ISSN 1022-1824.
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Official URL: https://doi.org/10.1007/s00029-021-00712-8
Abstract
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fun- damental relation to the geometric Robinson-Schensted-Knuth correspondence and to the geometric Schützenberger involution. We also show a number of properties of the geometric Burge correspondence, specializing them to the case of symmetric input arrays. In particular, our construction shows that such a mapping is volume preserving in log-log variables. As an application, we consider a model of two polymer paths of given length constrained to have the same endpoint, known as polymer replica. We prove that the distribution of the polymer replica partition function in a log-gamma random environment is a Whittaker measure, and deduce the corresponding Whittaker integral identity. For a certain choice of the parameters, we notice a distributional iden- tity between our model and the symmetric log-gamma polymer studied by O’Connell, Seppäläinen, and Zygouras (2014).
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Combinatorial analysis, Symmetric functions | |||||||||
Journal or Publication Title: | Selecta Mathematica, New Series | |||||||||
Publisher: | Birkhauser Verlag AG | |||||||||
ISSN: | 1022-1824 | |||||||||
Official Date: | 13 October 2021 | |||||||||
Dates: |
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Volume: | 27 | |||||||||
Article Number: | 100 | |||||||||
DOI: | 10.1007/s00029-021-00712-8 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 15 October 2021 | |||||||||
Date of first compliant Open Access: | 18 October 2021 | |||||||||
RIOXX Funder/Project Grant: |
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