Limit shapes for the asymmetric five vertex model
Probability
2022-06-10 v3
Abstract
We compute the free energy and surface tension function for the five-vertex model, a model of non-intersecting monotone lattice paths on the grid in which each corner gets a positive weight. We give a variational principle for limit shapes in this setting, and show that the resulting Euler-Lagrange equation can be integrated, giving explicit limit shapes parameterized by analytic functions.
Cite
@article{arxiv.1812.11934,
title = {Limit shapes for the asymmetric five vertex model},
author = {Jan de Gier and Richard Kenyon and Samuel S. Watson},
journal= {arXiv preprint arXiv:1812.11934},
year = {2022}
}
Comments
37 pages, 21 figures