2 1 Ja n 20 03 Epidemics , disorder , and percolation

Epidemics, disorder, and percolation

Spatial models for spread of an epidemic may be mapped onto bond percolation. We point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on the disorder because the critical region of the corresponding percolation model is broadened. In some networks the percola...

Ja n 20 08 Local Persistence in the Directed Percolation Universality Class

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we introduce a graded persistence probability that a site does not flip more than n times and demonstrate how local persistence can be stu...

Ja n 20 03 Scaling Limit , Noise , Stability

Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear functions and lead to nonclassical noises. Two examples are examined, Warren’s ‘noise made by a Poisson snake’ and the author’s ‘Brownian web as a black noise’. ...

ar X iv : h ep - t h / 03 01 12 7 v 1 1 7 Ja n 20 03 Supersymmetry in Spaces of Constant Curvature

ar X iv : m at h - ph / 0 60 10 23 v 1 1 1 Ja n 20 06 Cardy ’ s Formula for Certain Models of the Bond – Triangular Type

We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act independently of one another. By avoiding explicit use of microscopic paths, it is first established that the model possesses the typical attributes which are indic...