Date: 2016-03-10

Time: 15:30-16:30

Location: MAASS 217, McGill

Abstract:

It is well known that normal random variables do not like taking large values. Therefore, a continuous Gaussian random field on a compact set does not like exceeding a large level. If it does exceed a large level at some point, it tends to go back below the level a short distance away from that point. One, therefore, does not expect the excursion set above a high for such a field to possess any interesting structure. Nonetheless, if we want to know how likely are two points in such an excursion set to be connected by a path (“a ridge”) in the excursion set, how do we figure that out? If we know that a ridge in the excursion set exists (e.g. the field is above a high level on the surface of a sphere), how likely is there to be also a valley (e.g. the field going to below a fraction of the level somewhere inside that sphere)?

We use the large deviation approach. Some surprising results (and pictures) are obtained.

Speaker

Gennady Samorodnitsky is a Professor in the School of Operations Research and Information Engineering at Cornell. He is a distinguished probabilist with broad interests, including stochastic models, long-range dependence, random fields, scale-free random graphs and extreme-value theory.