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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 . (In Press)
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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 > 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 | |||||||||
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| Status: | Peer Reviewed | |||||||||
| Publication Status: | In Press | |||||||||
| Access rights to Published version: | Open Access | |||||||||
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