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.
| Original language | English |
|---|---|
| Pages (from-to) | 483-497 |
| Number of pages | 15 |
| Journal | Tohoku Mathematical Journal |
| Volume | 61 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 2009 |
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Keywords
- Branching brownian motion
- Ito's formula
- Localization
- Poisson random measure
- Random environment
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Localization for branching brownian motions in random environment. / Shiozawa, Yuichi.
In: Tohoku Mathematical Journal, Vol. 61, No. 4, 12.2009, p. 483-497.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Localization for branching brownian motions in random environment
AU - Shiozawa, Yuichi
PY - 2009/12
Y1 - 2009/12
N2 - 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.
AB - 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.
KW - Branching brownian motion
KW - Ito's formula
KW - Localization
KW - Poisson random measure
KW - Random environment
UR - http://www.scopus.com/inward/record.url?scp=77649280424&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77649280424&partnerID=8YFLogxK
U2 - 10.2748/tmj/1264084496
DO - 10.2748/tmj/1264084496
M3 - Article
VL - 61
SP - 483
EP - 497
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
SN - 0040-8735
IS - 4
ER -