English

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

R2 v1 2026-06-23T07:00:09.172Z