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

TL;DR

This paper investigates the convergence of high intensity shot noise fields to Gaussian fields, establishing a strong invariance principle and deriving asymptotic properties of percolation thresholds.

Contribution

It introduces a quantitative coupling between shot noise and Gaussian fields and provides an asymptotic expansion for the critical percolation level.

Findings

Established a strong invariance principle for high intensity shot noise fields.

Derived an asymptotic expansion for the critical percolation level.

Demonstrated uniform closeness of shot noise and Gaussian fields on large domains.

Abstract

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.