Branching brownian motion under soft killing

Name: Branching brownian motion under soft killing
Author: Oz, Mehmet

İsim	Branching brownian motion under soft killing
Yazar	Oz, Mehmet
Basım Tarihi:	2024-01-01
Basım Yeri	- IMPA
Konu	Soft killing, Poissonian traps, Law of large numbers, Random environment, Branching brownian motion
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1980-0436
Kayıt Numarası	1f02f81d-7df2-4ab2-9554-4ef983eb70d8
Lokasyon	Natural and Mathematical Sciences
Tarih	2024-01-01
Örnek Metin	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

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Branching brownian motion under soft killing

Yazar Oz, Mehmet

Basım Tarihi 2024-01-01

Basım Yeri - IMPA

Konu Soft killing, Poissonian traps, Law of large numbers, Random environment, Branching brownian motion

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1980-0436

Kayıt Numarası 1f02f81d-7df2-4ab2-9554-4ef983eb70d8

Lokasyon Natural and Mathematical Sciences

Tarih 2024-01-01

Örnek Metin 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