Branching brownian motion in an expanding ball and application to the mild obstacle problem

Name: Branching brownian motion in an expanding ball and application to the mild obstacle problem
Author: Oz, Mehmet

İsim	Branching brownian motion in an expanding ball and application to the mild obstacle problem
Yazar	Oz, Mehmet
Basım Tarihi:	2024-01-01
Basım Yeri	- Institute of Mathematical Statistics
Konu	Branching Brownian motion
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1083-6489
Kayıt Numarası	a312ab9a-3b70-41d6-b964-f9821593ce1a
Lokasyon	Natural and Mathematical Sciences
Tarih	2024-01-01
Örnek Metin	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

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Branching brownian motion in an expanding ball and application to the mild obstacle problem

Yazar Oz, Mehmet

Basım Tarihi 2024-01-01

Basım Yeri - Institute of Mathematical Statistics

Konu Branching Brownian motion

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1083-6489

Kayıt Numarası a312ab9a-3b70-41d6-b964-f9821593ce1a

Lokasyon Natural and Mathematical Sciences

Tarih 2024-01-01

Örnek Metin 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