Scholarlink

<p>We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points (such that the union of the triangles intersecting the interface does not separate the points) in the scaling limit. This generalizes both Cardy’s and Schramm’s formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Generalization of Cardy’s and Schramm’s Formulae

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月10日

查看全文
  • Mikhail Khristoforov,
  • Mikhail Skopenkov,
  • Stanislav Smirnov

摘要

We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points (such that the union of the triangles intersecting the interface does not separate the points) in the scaling limit. This generalizes both Cardy’s and Schramm’s formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping.