Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment

Multiscale analysis is a technique used in the study of disordered systems in the presence of phenomena similar to Griffiths singularities. In this article we illustrate the use of a multiscale analysis by applying it to a very simple model: percolation in a random environment. We also describe the application of this technique to continuous time percolation and contact processes in random environments.

[1]  Geoffrey Grimmett,et al.  Exponential decay for subcritical contact and percolation processes , 1991 .

[2]  A. Klein,et al.  A new proof of localization in the Anderson tight binding model , 1989 .

[3]  Robert B. Griffiths,et al.  Nonanalytic Behavior Above the Critical Point in a Random Ising Ferromagnet , 1969 .

[4]  Thomas M. Liggett,et al.  The Survival of One-Dimensional Contact Processes in Random Environments , 1992 .

[5]  F. Martinelli,et al.  Constructive proof of localization in the Anderson tight binding model , 1985 .

[6]  Maury Bramson,et al.  The Contact Processes in a Random Environment , 1991 .

[7]  J. Fröhlich,et al.  Absence of diffusion in the Anderson tight binding model for large disorder or low energy , 1983 .

[8]  A. Klein,et al.  Localization for random Schrödinger operators with correlated potentials , 1991 .

[9]  M. Aizenman,et al.  Percolation methods for disordered quantum Ising models , 1993 .

[10]  Enrique Andjel Survival of multidimensional contact process in random environments , 1992 .

[11]  T. Spencer Localization for random and quasiperiodic potentials , 1988 .

[12]  Kenneth S. Alexander,et al.  Spatial Stochastic Processes , 1991 .

[13]  T. Liggett Interacting Particle Systems , 1985 .

[14]  A. Klein,et al.  Localization in the ground state of the ising model with a random transverse field , 1991 .

[15]  Thomas M. Liggett,et al.  Spatially Inhomogeneous Contact Processes , 1991 .

[16]  A. Klein,et al.  Decay of two-point functions for (d+1)-dimensional percolation, ising and Potts models withd-dimensional disorder , 1991 .

[17]  Abel Klein,et al.  Ising model in a quasiperiodic transverse field, percolation, and contact processes in quasiperiodic environments , 1993 .

[18]  Localization in the ground state of a disordered array of quantum rotators , 1992 .

[19]  Abel Klein,et al.  EXTINCTION OF CONTACT AND PERCOLATION PROCESSES IN A RANDOM ENVIRONMENT , 1994 .