Related papers: Notes on oriented percolation
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.
Despite the growing interest in diffusion models, gaining a deep understanding of the model class remains an elusive endeavour, particularly for the uninitiated in non-equilibrium statistical physics. Thanks to the rapid rate of progress in…
We correct a simple error in Percolation on random Johnson-Mehl tessellations and related models, Probability Theory and Related Fields 140 (2008), 417-468. (See also arXiv:math/0610716)
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…
In this chapter of the e-book "Self-Organized Criticality Systems" we summarize some theoretical approaches to self-organized criticality (SOC) phenomena that involve percolation as an essential key ingredient. Scaling arguments, random…
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…
The aim of this note is to show that many papers on various kinds of filters (and related concepts) in (subreducts of) residuated structures are in fact easy consequences of more general results that have been known for a long time.
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
The purpose of the present note is to review and improve the convergence of the renormalized winding fields.
We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable…
In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…