- 09-119 Yukio Nagahata and Nobuo Yoshida
- Localization for a Class of Linear Systems
Jul 23, 09
(auto. generated ps),
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Abstract. We consider a class of continuous-time stochastic growth models on
$d$-dimensional lattice with non-negative real numbers
as possible values per site. The class contains examples such as binary contact path process and potlatch process.
We show the equivalence between theslow population growth and localization property that the time integral of the replica overlap diverges. We also prove, under reasonable assumptions, a
localization property in a stronger form that the spatial distribution of the population does not decay uniformly in space.