Limit shapes for the asymmetric five vertex model

Jan de Gier; Richard Kenyon; Samuel S. Watson

doi:10.1007/s00220-021-04126-7

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arXiv · 1812.11934

Limit shapes for the asymmetric five vertex model

Jan de Gier·Richard Kenyon·Samuel S. Watson

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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.

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Jan de Gier, Richard Kenyon, Samuel S. Watson. 2018-12-31. Limit shapes for the asymmetric five vertex model. https://doi.org/10.1007/s00220-021-04126-7

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