Invariance of polymer partition functions under the geometric RSK correspondence
Probability
2020-03-04 v2 Combinatorics
Abstract
We prove that the values of discrete directed polymer partition functions involving multiple non-intersecting paths remain invariant under replacing the background weights by their images under the geometric RSK correspondence. This result is inspired by a recent and remarkable identity proved by Dauvergne, Orthmann and Vir\'ag which is recovered as the zero-temperature, semi-discrete limit of our main result.
Keywords
Cite
@article{arxiv.2001.01867,
title = {Invariance of polymer partition functions under the geometric RSK correspondence},
author = {Ivan Corwin},
journal= {arXiv preprint arXiv:2001.01867},
year = {2020}
}
Comments
35 pages, 19 figures. Two new proofs of the main result are provided in this revision