Six-vertex model with rare corners and random restricted permutations

• 成果类型: Article
• 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; 1432-2064
• DOI: 10.1007/s00440-025-01382-9
• 发表日期: 2026-04
• 页码: 2193-2234
• 关键词: domino tilings

摘要

We study limit shapes in two equivalent models: the six-vertex model in the c -> 0 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.