On bulk deviations for the local behavior of random interlacements

Abstract

We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing local function of the field of occupation times, sampled at each point of a large box, exceeds its expected value. We express the exponential rate of decay in terms of a constrained minimum for the Dirichlet energy of functions on R^d that decay at infinity. An application concerns the excess presence of random interlacements in a large box. Our findings exhibit similarities to some of the results of van den Berg-Bolthausen-den Hollander in their work on moderate deviations of the volume of the Wiener sausage. An other application relates to recent work of the author on macroscopic holes in connected components of the vacant set in arXiv:1802.05255v2.

57 pages, 1 figure, to appear in Annales Scientifiques de l' École Normale Supérieure

References in corpus (5)

• 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 macroscopic holes in some supercritical strongly dependent percolation models
• Geometry of Gaussian free field sign clusters and random interlacements
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Cited by in corpus (5)

• Excess deviations for points disconnected by random interlacements
• 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
• Moderate deviations for the range of a transient random walk. II