Author
Oz, Mehmet
Publication Date
2024-01-01
Publication Place
-
Institute of Mathematical Statistics
Subject
Branching Brownian motion
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1083-6489
Record ID
a312ab9a-3b70-41d6-b964-f9821593ce1a
Library Location
Natural and Mathematical Sciences
Date
2024-01-01
Sample Text
We first study a d-dimensional branching Brownian motion (BBM) among mild Poisso-nian obstacles, where a random trap field in Rd is created via a Poisson point process. The trap field consists of balls of fixed radius centered at the atoms of the Poisson point process. The mild obstacle rule is that when particles are inside traps, they branch at a lower rate, which is allowed to be zero, whereas when outside traps they branch at the normal rate. We prove upper bounds on the large-deviation probabilities for the total mass of BBM among mild obstacles, which we then use along with the Borel-Cantelli lemma to prove the corresponding strong law of large numbers. Our results are quenched, that is, they hold in almost every environment with respect to the Poisson point process. Our strong law improves on the existing corresponding weak law in [Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), 490–518]. We also study a d-dimensional BBM inside subdiffusively expanding balls, where the boundary of the ball is deactivating in the sense that once a particle of the BBM hits the moving boundary, it is instantly deactivated but will be reactivated at a later time provided its ancestral line is fully inside the expanding ball at that later time. We obtain a large-deviation result as time tends to infinity on the probability that the mass inside the ball is aytpically small. An essential ingredient in the proofs of the strong law of large numbers for BBM among mild obstacles turns out to be the large-deviation result on the mass of BBM inside expanding balls.
DOI
10.1214/24-EJP1112
Cilt
29
