Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields

被引：0

作者：

Lachieze-Rey, Raphael ^{[1
]}

Muirhead, Stephen ^{[2
]}

机构：

[1] Univ Paris Cite, Paris, France

[2] Univ Melbourne, Sch Math & Stat, Melbourne, Australia

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2023年 / 59卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Shot noise fields; Gaussian fields; Percolation; Strong invariance principle; STRONG APPROXIMATION; PHASE-TRANSITION; PERCOLATION; CONVERGENCE; UNIQUENESS; CROSSINGS; VARIABLES; SETS; LAWS;

D O I：

10.1214/22-AIHP1303

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 study fine properties of the convergence of a high intensity shot noise field towards the Gaussian field with the same covariance structure. In particular we (i) establish a strong invariance principle, i.e. a quantitative coupling between a high intensity shot noise field and the Gaussian limit such that they are uniformly close on large domains with high probability, and (ii) use this to derive an asymptotic expansion for the critical level above which the excursion sets of the shot noise field percolate.

引用

页码：1375 / 1397

页数：23

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