Related papers: The OSSS Method in Percolation Theory
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…
The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is…
The percolation of a liquid through a porous material is investigated with the help of equations of the Onsager type. An expression is derived for the molecular attraction, starting from Sutherland's potential approximation to the van der…
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
The charge transport mechanism in amorphous oxide semiconductors (AOS) is a matter of controversial debates. Most theoretical studies so far neglected the percolation nature of the phenomenon. In this article, a recipe for theoretical…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
In this work, percolation properties of device-to-device (D2D) networks in urban environments are investigated. The street system is modeled by a Poisson-Delaunay triangulation (PDT). Users are of two types: given either by a Cox process…
We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap…
In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At…
We describe the percolation model and some of the principal results and open problems in percolation theory. We also discuss briefly the spectacular recent progress by Lawler, Schramm, Smirnov and Werner towards understanding the phase…
We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our…
Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an $O(1)$-window) for…
This review aims to provide a simple introduction to the application of optical correlation methods in colloidal science. In particular, I plan to show that full appraisal of the intimate relation between light scattering and microscopy…
Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
This paper seeks to synthesize much recent work on the HTSC materials around the latest energy resolved scanning tunnelling microscopy (STM) results from Davis and coworkers. The STM conductance diffuse scattering results in particular are…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
This paper seeks to synthesize much recent work on the HTSC materials around the latest energy resolved scanning tunnelling microscopy (STM) results from Davis and coworkers. The conductance diffuse scattering results in particular are…
A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.
Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of…