Web1 de nov. de 2013 · In particular, a QIP thus holds for random walks on long-range percolation graphs with connectivity exponents larger than 2d in all \(d\ge 2\), provided … Web8 de jun. de 2024 · We study long-range Bernoulli percolation on $${\\mathbb {Z}}^d$$ Z d in which each two vertices x and y are connected by an edge with probability $$1-\\exp (-\\beta \\Vert x-y\\Vert ^{-d-\\alpha })$$ 1 - exp ( - β ‖ x - y ‖ - d - α ) . It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if $$0<\\alpha

PERCOLATION English meaning - Cambridge Dictionary

Web8 de jun. de 2015 · Recently, by introducing the notion of cumulatively merged partition, Ménard and Singh provide a sufficient condition on graphs ensuring that the critical value of the contact process is positive. In this note, we show that the one-dimensional long range percolation with high exponent satisfies their condition and thus the contact process … The most common percolation model is to take a regular lattice, like a square lattice, and make it into a random network by randomly "occupying" sites (vertices) or bonds (edges) with a statistically independent probability p. At a critical threshold pc, large clusters and long-range connectivity first appears, and this is called the percolation threshold. Depending on the method for obtaining the random network, one distinguishes between the site percolation threshold and the bond … january subscription boxes

[1103.0208] Scale-free percolation - arXiv

Web12 de dez. de 2024 · We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on \({\mathbb{Z}^d}\) (\({d \geq 2}\)).The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the … Web16 de mar. de 2013 · Distances in critical long range percolation. Jian Ding, Allan Sly. We study the long range percolation model on where sites and are connected with … Web4 de ago. de 2011 · Abstract. In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation … january suitcase