08-195 Nobuo YOSHIDA

Localization for Linear Stochastic Evolutions (213K, pdf) Oct 23, 08

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Abstract. We consider a discrete-time stochastic growth model on $d$-dimensional lattice. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process. We show the equivalence between the slow population growth and a localization property in terms of ``replica overlap". This extends a result known for the directed polymers in random environment to a large class of models. A new approach, based on the multiplicative Doob's decomposition, is adopted to overcome the difficulty that the total population may get extinct even at finite time.

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