Six-vertex model with rare corners and random restricted permutations
成果类型：
Article; Early Access
署名作者：
Gorin, Vadim; Kenyon, Richard
署名单位：
University of California System; University of California Berkeley; Yale University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-025-01382-9
发表日期：
2025
关键词：
摘要：
We study limit shapes in two equivalent models: the six-vertex model in the c -> 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c\rightarrow 0$$\end{document} 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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