Invariance of polymer partition functions under the geometric RSK correspondence
arXiv:2001.01867
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 Virág which is recovered as the zero-temperature, semi-discrete limit of our main result.
35 pages, 19 figures. Two new proofs of the main result are provided in this revision