Related papers: On large deviations and intersection of random int…
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…
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…
We consider the vacant set of random interlacements on Z^d, with d bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work arXiv:1304.7477, we investigate the asymptotic…
We consider random interlacements on Z^d, with d bigger or equal to 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of…
The main focus of this article concerns the strongly percolative regime of the vacant set of random interlacements on $ \mathbb{Z}^d$, with $d \ge 3$. We investigate the occurrence in a large box of an excessive fraction of sites that get…
We consider $Z^d$, with d bigger or equal to three. We investigate the vacant set of random interlacements in the strongly percolative regime, the vacant set of the simple random walk, and the excursion set above a given level of the…
We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of Z^d, with d bigger or equal to 3. As an application, we analyze the asymptotic behavior of the…
We prove a conditional decoupling inequality for the model of random interlacements in dimension $d\geq 3$: the conditional law of random interlacements on a box (or a ball) $A_1$ given the (not very "bad") configuration on a "distant" set…
We investigate percolation of the vacant set of random interlacements on $\mathbb{Z}^d$, $d\geq 3$, in the strongly percolative regime. We consider the event that the interlacement set at level $u$ disconnects the discrete blow-up of a…
We obtain large deviations estimates for the self-intersection local times for a symmetric random walk in dimension 3. Also, we show that the main contribution to making the self-intersection large, in a time period of length $n$, comes…
In this paper we establish some properties of percolation for the vacant set of random interlacements, for d at least 5 and small intensity u. The model of random interlacements was first introduced by A.S. Sznitman in arXiv:0704.2560. It…
We consider continuous time random interlacements on $\mathbb{Z}^d$, $d \ge 3$, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the…
We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the models of scale-free percolation, the Boolean model with…
We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z^d, d bigger or equal to 3. A non-negative parameter u measures how many trajectories enter the picture. This model describes in the…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
Random interlacements at level u is a one parameter family of connected random subsets of Z^d, d>=3 introduced in arXiv:0704.2560. Its complement, the vacant set at level u, exhibits a non-trivial percolation phase transition in u, as shown…
We investigate random interlacements on Z^d, d bigger or equal to 3. This model recently introduced in arXiv:0704.2560 corresponds to a Poisson cloud on the space of doubly infinite trajectories modulo time-shift tending to infinity at…