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Publications in Scientific Journals:

E. Bisi, N. O´Connell, N. Zygouras:
"The geometric Burge correspondence and the partition function of polymer replicas";
Selecta Mathematica New Series, 27 (2021), art.100; 1 - 39.



English 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 fundamental 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 identity between our model and the symmetric log-gamma polymer studied by O´Connell, Seppäläinen, and Zygouras (2014).


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/s00029-021-00712-8


Created from the Publication Database of the Vienna University of Technology.