Department seminar by Yi Shen

Please Note: This seminar will be given online.

Excursion sets and critical points of Gaussian random fields over high thresholds

In this talk we discuss the excursion sets and the location and type of the critical points of isotropic Gaussian random fields satisfying certain conditions over high thresholds. We show that for these Gaussian random fields, when the threshold tends to infinity and the searching area expands with a matching speed, both the location of the excursion sets and the location of the local maxima above the threshold converge weakly to a Poisson point process. We will further discuss the possibility to approximate these locations when the threshold is high but not extremely high, by studying the local behavior of the critical points above the threshold of the random field. This is a joint work with Paul Marriott and Weinan Qi.