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Localization for a Class of Linear Systems
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Yukio Nagahata, Department of mathematics, Graduate School of Engineering Science Osaka Universi
Nobuo Yoshida, Division of Mathematics Graduate School of Science Kyoto University
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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 the
slow 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.
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Full text: PDF
Pages: 636-653
Published on: May 17, 2010
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Electronic Journal of Probability. ISSN: 1083-6489 |
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