关于二维临界渗流垫圈和锚定集群的密度

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-03-15 DOI:10.1007/s11005-024-01793-0

Federico Camia

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引用次数: 0

摘要

摘要我们证明了 Kleban、Simmons 和 Ziff 利用共形场论方法首次获得的上半平面临界渗滤簇 "锚定 "于实线上一点的（重规范化）密度公式。证明受到了图像方法的启发。我们还证明了更一般的体界连接概率具有定义明确的尺度协变缩放极限，并证明了与单位盘保形等价的任何域中临界渗滤簇（重归一化）密度的缩放极限公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the density of 2D critical percolation gaskets and anchored clusters

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On the density of 2D critical percolation gaskets and anchored clusters

We prove a formula, first obtained by Kleban, Simmons and Ziff using conformal field theory methods, for the (renormalized) density of a critical percolation cluster in the upper half-plane “anchored” to a point on the real line. The proof is inspired by the method of images. We also show that more general bulk-boundary connection probabilities have well-defined, scale-covariant scaling limits and prove a formula for the scaling limit of the (renormalized) density of the critical percolation gasket in any domain conformally equivalent to the unit disk.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.