Electronic Journal of Probability

Localization for a Class of Linear Systems

Yukio Nagahata and Nobuo Yoshida

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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.

Article information

Electron. J. Probab., Volume 15 (2010), paper no. 20, 636-653.

Accepted: 17 May 2010
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes

localization linear systems binary contact path process potlatch process

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Nagahata, Yukio; Yoshida, Nobuo. Localization for a Class of Linear Systems. Electron. J. Probab. 15 (2010), paper no. 20, 636--653. doi:10.1214/EJP.v15-757. https://projecteuclid.org/euclid.ejp/1464819805

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