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In this talk, we will show several results for correlated nearest neighbor site percolation on Z^d. In particular, we will show that in three dimensions the strongly correlated massless harmonic cryst...
In this lecture, I will discuss some of the recent progresses in the level-set percolation of Gaussian free field in (d\geq 3), including the positivity of threshold and (if time permits) sharp phase ...
In this lecture, I will discuss some of the recent progresses in the level-set percolation of Gaussian free field in (d\geq 3), including the positivity of threshold and (if time permits) sharp phase ...
In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor's ideas and describes infinite an...
While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are lar...
We consider directed random walk on the infinite percolation cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the `ancestral lineage' of an individu...
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for h...
We study the influences of antidot-induced bound states on transport properties of two- dimensional quantum spin Hall insulators. The bound statesare found able to induce quantum percolation in the or...
Abstract: We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains u...
Abstract: Secrecy graphs model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presenc...
Abstract: In this paper we consider first-passage percolation on certain subgraphs of the $\Z^d$ nearest neighbour graph. We present a three-fold extension of the Shape Theorem. Firstly, we show that ...
Abstract: In this paper we consider standard first-passage percolation on certain 1-dimensional periodic graphs. One such graph of particular interest is the $\Z\times\{0,1,...,K-1\}^{d-1}$ nearest ne...
Abstract: We numerically investigate the conductivities of continuum percolation models consisting of overlapped particles using the finite difference method as a sequel of our previous article (Int. ...
Abstract: In $\HH$-bootstrap percolation, a set $A \subset [n]$ of initially `infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph $\HH \s...
Abstract: Graph bootstrap percolation is a deterministic cellular automaton which was introduced by Bollob\'as in 1968, and is defined as follows. Given a graph $H$, and a set $G \subset E(K_n)$ of in...

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