Author
Oz, Mehmet
Publication Date
2024-01-01
Publication Place
-
IMPA
Subject
Soft killing, Poissonian traps, Law of large numbers, Random environment, Branching brownian motion
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1980-0436
Record ID
1f02f81d-7df2-4ab2-9554-4ef983eb70d8
Library Location
Natural and Mathematical Sciences
Date
2024-01-01
Sample Text
We study a d-dimensional branching Brownian motion (BBM) among Poissonian obstacles, where a random trap field in R-d is created via a Poisson point process. In the soft obstacle model, the trap field consists of a positive potential which is formed as a sum of a compactly supported bounded function translated at the atoms of the Poisson point process. Particles branch at the normal rate outside the trap field; and when inside the trap field, on top of complete suppression of branching, particles are killed at a rate given by the value of the potential. Under soft killing, the probability that the entire BBM goes extinct due to killing is positive in almost every environment. Conditional on ultimate survival of the process, we prove a law of large numbers for the total mass of BBM among soft Poissonian obstacles. Our result is quenched, that is, it holds in almost every environment with respect to the Poisson point process.
DOI
10.30757/ALEA.v20
Cilt
21
