Excess deviations for points disconnected by random interlacements

Abstract

We consider random interlacements on ${\mathbb{Z}}^d$, $d\ge 3$, when their vacant set is in a strongly percolative regime. Given a large box centered at the origin, we establish an asymptotic upper bound on the exponential rate of decay of the probability that the box contains an excessive fraction $\nu$ of points that are disconnected by random interlacements from the boundary of a concentric box of double size. As an application we show that when $\nu$ is not too large, this asymptotic upper bound matches the asymptotic lower bound derived in a previous work of the author, and the exponential rate of decay is governed by a certain variational problem in the continuum which involves the percolation function of the vacant set of random interlacements.

arXiv comment46 pages, 3 figures, to appear in Probability and Mathematical Physics

References in corpus (9)

• Soft local times and decoupling of random interlacements
• On the uniqueness of the infinite cluster of the vacant set of random interlacements
• Equality of critical parameters for percolation of Gaussian free field level-sets
• On large deviations for the cover time of two-dimensional torus
• On macroscopic holes in some supercritical strongly dependent percolation models
• Solidification of porous interfaces and disconnection
• Percolation in the Harmonic Crystal and Voter Model in three dimensions
• Disconnection by level sets of the discrete Gaussian free field and entropic repulsion
• On bulk deviations for the local behavior of random interlacements

Cited by in corpus (5)

• Disconnection and entropic repulsion for the harmonic crystal with random conductances
• Analyticity of Gaussian free field percolation observables
• On the cost of the bubble set for random interlacements
• Percolation of strongly correlated Gaussian fields I. Decay of subcritical connection probabilities
• Phase transition for level-set percolation of the membrane model in dimensions $d\ge 5$