Localization for Linear Stochastic Evolutions

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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.

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Details 詳細情報について

  • CRID
    1050845760584633216
  • NII Article ID
    120002036597
  • NII Book ID
    AA00707889
  • ISSN
    00224715
  • HANDLE
    2433/108361
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • IRDB
    • CiNii Articles

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