Localization for Linear Stochastic Evolutions

Access this Article

Search this Article

Author(s)

Abstract

We consider a discrete-time stochastic growth model on the d-dimensional lattice with non-negative real numbers as possible values per site. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of the binary contact path process. We show the equivalence between the slow population growth and a localization property in terms of "replica overlap". The main novelty of this paper is that we obtain this equivalence even for models with positive probability of extinction at finite time. In the course of the proof, we characterize, in a general setting, the event on which an exponential martingale vanishes in the limit.

Journal

  • Journal of Statistical Physics

    Journal of Statistical Physics 138(4-5), 598-618, 2010-03

    Springer Verlag

Codes

  • NII Article ID (NAID)
    120002036597
  • NII NACSIS-CAT ID (NCID)
    AA00707889
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0022-4715
  • Data Source
    IR 
Page Top