A0586
Title: Excursion sets and critical points of Gaussian random fields over high thresholds
Authors: Yi Shen - University of Waterloo (Canada) [presenting]
Weinan Qi - University of Waterloo (Canada)
Paul Marriott - University of Waterloo (Canada)
Abstract: The excursion sets and the location and type of the critical points of isotropic Gaussian random fields are discussed, satisfying certain conditions over high thresholds. After quickly introducing the Poisson limit result for the critical points and the excursion sets as the threshold tends to infinity, a discussion of the local behavior of the critical points is proceeded with, and it is shown that a pair of close critical points in $R^n$, both above a high threshold, predominantly consists of one local maxima and one saddle point with index n-1. The possibility of approximating these locations when the threshold is high but not extremely high is also possible and is further discussed.
