Tohoku Mathematical Journal
2009
December
SECOND SERIES VOL. 61, NO. 4

Tohoku Math. J.
61 (2009), 483-497

Title LOCALIZATION FOR BRANCHING BROWNIAN MOTIONS IN RANDOM ENVIRONMENT

Author Yuichi Shiozawa

(Received January 23, 2009, revised June 15, 2009)
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.

2000 Mathematics Subject Classification. Primary 60K37; Secondary 60G44, 60G57, 60J80.
Key words and phrases. Branching Brownian motion, random environment, localization, Poisson random measure, Ito's formula.

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