Nobuo YOSHIDA
Localization for Linear Stochastic Evolutions
(213K, pdf)

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.