Disconnection and level-set percolation for the Gaussian free field

Abstract

We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on the probability that the excursion-set of the Gaussian free field below the level alpha disconnects a box of large side-length from the boundary of a larger homothetic box. It remains an open question whether our asymptotic upper and lower bounds are matching. With the help of a recent work of Lupu, see arXiv:1402.0298, we are able to infer some asymptotic upper bounds for similar disconnection problems by random interlacements, or by simple random walk.

40 pages, has appeared in the special issue of the J. Math. Soc. Japan on the centennial of the birth of Kiyosi Ito

References in corpus (3)

• On decoupling inequalities and percolation of excursion sets of the Gaussian free field
• A lower bound for disconnection by random interlacements
• On the disconnection of a discrete cylinder by a biased random walk

Cited by in corpus (1)

• A lower bound for disconnection by simple random walk