Six-vertex model with rare corners and random restricted permutations

Vadim Gorin; Richard Kenyon

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arXiv · 2408.14446

Six-vertex model with rare corners and random restricted permutations

Vadim Gorin·Richard Kenyon

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Abstract

We study limit shapes in two equivalent models: the six-vertex model in the $c\to0$ 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.

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Vadim Gorin, Richard Kenyon. 2024-08-26. Six-vertex model with rare corners and random restricted permutations. https://arxiv.org/abs/2408.14446

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