Seminar at SMU Delhi
February 16, 2012 (Thursday) ,
11:30 AM at Webinar
Weizmann Institute of Science, Israel
Branching Random Walks and the Maxima of Gaussian Free Fields
Abstract of Talk
Bramson and the speaker considered the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and proved (2011) that its maximum, centered at its mean, is tight, settling a long standing conjecture. The proof exploits similarities with branching random walks, and combines an argument of Dekking and Host (1991), adapted by Bolthausen, Deuschel and the speaker to the GFF setup (2010) with elements from Bramson's thesis (1978) and comparison theorems for Gaussian fields. An essential part of the argument is the precise evaluation, up to an error of order 1, of the expected value of the maximum of the GFF in a box. Related Gaussian fields, such as the GFF on a two dimensional torus, are also discussed. Finally, I will discuss some recent progress concerning non-homogeneous branching random walks, and links with the cover time of graphs by random walks.