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

Abstract

It is known that the global connectivity of the excursion sets of shot noise fields undergoes a percolation phase transition at a certain critical level, which depends on the intensity of the underlying Poisson point process. In this paper we study the asymptotic expansion of the critical level in the high intensity limit. A key input is a strong invariance principle for shot noise fields, i.e. a quantitative coupling between a high intensity shot noise field and the Gaussian field with the same covariance, which is of independent interest.