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<p>We study limit shapes in two equivalent models: the six-vertex model in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c\rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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Six-vertex model with rare corners and random restricted permutations

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Vadim Gorin,
  • Richard Kenyon

摘要

We study limit shapes in two equivalent models: the six-vertex model in the \(c\rightarrow 0\) 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.