Related papers: Conditional decoupling of random interlacements
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…
We investigate random interlacements on $\mathbb{Z}^d$ with $d \geq 3$, and derive the large deviation rate for the probability that the capacity of the interlacement set in a macroscopic box is much smaller than that of the box. As an…
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…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…
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…
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 establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin,…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
In this paper we obtain a decoupling feature of the random interlacements process $\mathcal{I}^u \subset \mathbb{Z}^d$, at level $u$, $d\geq 3$. More precisely, we show that the trace of the random interlacements process on two disjoint…
We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detailed information about their geometry, and the percolative…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz norms), tail…
We prove a law of large numbers for certain random walks on certain attractive dynamic random environments when initialised from all sites equal to the same state. This result applies to random walks on $\mathbb{Z}^d$ with $d\geq1$. We…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
In this paper we establish a decoupling feature of the random interlacement process I^u in Z^d, at level u, for d \geq 3. Roughly speaking, we show that observations of I^u restricted to two disjoint subsets A_1 and A_2 of Z^d are…
We show that under certain assumptions one can derive a variant of Specker's non-contextual inequality for a system of three indistinguishable bosonic particles. The inequality states that the sum of probabilities of three pairwise…
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…