Localization for branching Brownian motions in random environment

Localization for branching Brownian motions in random environment

Yuichi Shiozawa

Source: Tohoku Math. J. (2) Volume 61, Number 4 (2009), 483-497.

Abstract

We consider a model of branching Brownian motions in random environment associated with the Poisson random measure. We find a relation between the slow population growth and the localization property in terms of the replica overlap. Applying this result, we prove that, if the randomness of the environment is strong enough, this model possesses the strong localization property, that is, particles gather together at small sets.

First Page: Show

Primary Subjects: 60K37

Secondary Subjects: 60G44, 60G57, 60J80

Keywords: Branching Brownian motion; random environment; localization; Poisson random measure; Ito's formula

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.tmj/1264084496
Digital Object Identifier: doi:10.2748/tmj/1264084496
Zentralblatt MATH identifier: 05687940
Mathematical Reviews number (MathSciNet): MR2598246

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