Percolation of the excursion sets of planar symmetric shot noise fields

被引：4

作者：

Lachieze-Rey, Raphael ^{[1
,2
]}

Muirhead, Stephen ^{[3
,4
]}

机构：

[1] Univ Paris 05, Paris, France

[2] Univ Paris, Paris, France

[3] Queen Mary Univ London, Sch Math Sci, London, England

[4] Univ Melbourne, Sch Math & Stat, Melbourne, Vic, Australia

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2022年 / 147卷

基金：

澳大利亚研究理事会;

关键词：

Percolation; Excursion sets; Shot noise fields; Phase transition; PHASE-TRANSITION; SENSITIVITY; UNIQUENESS; PERIMETER; GEOMETRY;

D O I：

10.1016/j.spa.2022.01.013

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove the existence of phase transitions in the global connectivity of the excursion sets of planar symmetric shot noise fields. Our main result establishes a phase transition with respect to the level for shot noise fields with symmetric log-concave mark distributions, including Gaussian, uniform, and Laplace marks, and kernels that are positive, symmetric, and have sufficient tail decay. Without the log-concavity assumption we prove a phase transition with respect to the intensity of positive marks. (C) 2022 Elsevier B.V. All rights reserved.

引用

页码：175 / 209

页数：35

共 31 条

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