Related papers: Continuum percolation for Gibbs point processes
We consider some continuum percolation models. We are mainly interested in giving some sufficient conditions for absence of percolation. We give some general conditions and then focuse on two examples. The first one is a multiscale…
We consider the Poisson Boolean model of continuum percolation on a homogeneous Riemannian manifold $M$. Let $lambda$ be intensity of the Poisson process in the model and let $lambda_u$ be the infimum of the set of intensities that a.s.…
We investigate locality of the supercritical regime for Bernoulli percolation on transitive graphs with polynomial growth, by which we mean the following. Take a transitive graph of polynomial growth $\mathscr{G}$ satisfying…
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…
Let $\Xi$ be the set of points (we call the elements of $\Xi$ centers) of Poisson process in $\R^d$, $d\geq 2$, with unit intensity. Consider the allocation of $\R^d$ to $\Xi$ which is stable in the sense of Gale-Shapley marriage problem…
We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion…
A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \cite{G} in the context of the contact process in continuous time. As discussed here, it also…
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition…
This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals…
We consider bond and site Bernoulli Percolation in both the oriented and the non-oriented cases on $\mathbb{Z}^d$ and obtain rigorous upper bounds for the critical points in those models for every dimension $d \geq 3$.
This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry. First, we show the existence of Gibbs facet processes in…
We present the first experimental observations of scale-free behavior in the bubble footprint distribution during the boiling crisis of water, in pool and flow boiling conditions. We formulate a continuum percolation model that elucidates…
We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the…
In this paper, we study invariant Poisson processes of lines (i.e, bi-infinite geodesics) in the $3$-regular tree. More precisely, there exists a unique (up to multiplicative constant) locally finite Borel measure on the space of lines that…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. This is a special case of a conjecture due to O.…
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…
We study directed percolation at the upper critical transverse dimension $d=4$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address…
We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act…
If the specific angular momentum of accretion gas at large radius is small compared to the local Keplerian value, one usually believes that there exists a "circularization radius" beyond which the angular momentum of accretion flow is…