Ridges and valleys in the high excursion sets of Gaussian random fields

03/10/2016 - 15:30
03/10/2016 - 16:30
Gennady Samorodnitsky,(Cornell University)
McGill University, 801 Sherbrooke St. West, Otto Maass Building , Room: MAASS 217

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.

Last edited by on Mon, 03/07/2016 - 10:40