Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field

Details Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field

2011-05-29

arxiv.org/abs/1105.5833v2

Mathematics

Probability

12 pages, included Lemma 2.2 for the sake of completeness due to a comment of Sourav Chatterjee

Scientific paper

We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay for the left tail. In particular, our result implies that the variance of the maximum is of order 1, improving an $o(\log n)$ bound by Chatterjee (2008) and confirming a folklore conjecture. An important ingredient for our proof is a result of Bramson and Zeitouni (2010), who proved the tightness of the centered maximum together with an evaluation of the expectation up to an additive constant.

Affiliated with

Also associated with

No associations

Rating

Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-676979