We prove the statement in the title of the paper.

We show quenched large deviations for the simple random walk on percolation models with long-range correlations defined by Drewitz, Ráth and Sapozhnikov [3], which contain supercritical Bernoulli percolations, random interlacements, the vacant set of random interlacements and the level set of the Gaussian free field. Our result is an extension of Kubota’s result [8] for supercritical Bernoulli ...

In this article we study percolation on the Cayley graph of a free product of groups. Such a graph has a tree-like structure which allows us to evaluate the critical values of the phase transition, mean cluster size and the critical exponent in bond percolation.

This letter investigates the multiple routes transmitted epidemic process on multiplex networks. We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the epidemic can spread across the multiplex network even if all the network layers are well below their respective epidemic thresholds. Strong positive degree-d...

In this talk, we consider an oriented percolation model in a random environment, this model was proposed and studied by Kesten, Sidoravicius and Vares in [4]. Consider the following North-East oriented site percolation model on Z+. Given the parameters δ, p and ∆ ∈ [0, 1], for each line Hi := {(x, y) ∈ Z+;x+y = i}, ∀i ∈ Z+ we associate the 0-1 (‘good’ or ‘bad’) random variable, ξi, independentl...

In this paper, the study of bond percolation on the square lattice is explored. In particular, the probability at which there exist infinite clusters on an inhomogeneous model of the square lattice is proven from the basics used to prove the model with equal probabilities.

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of massM to sample size L as generally accepted for isotropic lattice problems, but with a p...

INTRODUCTION The percolation theory studies the critical points or percolation thresholds of the system, where one component of the system undergoes a geometrical phase transition, starting to connect the whole system.The application of this theory to study the release rate of hydrophilic matrices allows to explain the changes in release kinetics of swellable matrix type system and results in a...

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic susceptible-infectious-removed (SIR) epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because und...