4.5 Article

ON THE RADIUS OF GAUSSIAN FREE FIELD EXCURSION CLUSTERS

Journal

ANNALS OF PROBABILITY
Volume 50, Issue 5, Pages 1675-1724

Publisher

INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/22-AOP1569

Keywords

Gaussian free field; percolation; random walk; capacity

Funding

  1. ERC Grant CriBLaM
  2. IDEX grant from Paris-Saclay
  3. SERB [SRG/2021/000032]
  4. Infosys Foundation
  5. Swiss FNS

Ask authors/readers for more resources

This paper considers the Gaussian free field phi on Z(d), and provides sharp bounds on the probability of the radius of a finite cluster exceeding a given value for any height. The results show the decay rate of this probability in different dimensions.
We consider the Gaussian free field phi on Z(d), for d >= 3, and give sharp bounds on the probability that the radius of a finite cluster in the excursion set {phi >= h} exceeds a large value N for any height h not equal h(*), where h(*) refers to the corresponding percolation critical parameter. In dimension 3, we prove that this probability is subexponential in N and decays as exp{-pi/6 (h - h(*))(2) N/logN} as N -> infinity to principal exponential order. When d >= 4, we prove that these tails decay exponentially in N. Our results extend to other quantities of interest, such as truncated two-point functions and the two-arms probability for annuli crossings at scale N.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.5
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available