Six-vertex model with rare corners and random restricted permutations
Probability
2025-04-04 v2 Mathematical Physics
math.MP
Abstract
We study limit shapes in two equivalent models: the six-vertex model in the limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve it for a class of rectilinear polygonal domains. Its solutions are given by piecewise-algebraic functions with lines of discontinuities.
Keywords
Cite
@article{arxiv.2408.14446,
title = {Six-vertex model with rare corners and random restricted permutations},
author = {Vadim Gorin and Richard Kenyon},
journal= {arXiv preprint arXiv:2408.14446},
year = {2025}
}