Subdiffusivity of brownian motion among a poissonian field of moving traps

Name: Subdiffusivity of brownian motion among a poissonian field of moving traps
Author: Öz, Mehmet

İsim	Subdiffusivity of brownian motion among a poissonian field of moving traps
Yazar	Öz, Mehmet
Basım Tarihi:	2019
Basım Yeri	- Instituto Nacional de Matematica Pura e Aplicada
Konu	Brownian motion in random environment, Poissonian traps, Moving trap field, Subdiffusive, Optimal survival strategy
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1980-0436
Kayıt Numarası	7ddc96f8-2747-4452-8779-08606b9f176f
Lokasyon	Natural and Mathematical Sciences
Tarih	2019
Örnek Metin	Our model consists of a Brownian particle X moving in N, where a Poissonian field of moving traps is present. Each trap is a ball with constant radius, centered at a trap point, and each trap point moves under a Brownian motion independently of others and of the motion of X. Here, we investigate the 'speed' of X on the time interval [0, t] and on 'microscopic' time scales given that X avoids the trap field up to time t. Firstly, following the earlier work of 'Athreya. et al. (2017), we obtain bounds on the maximal displacement of X from the origin. Our upper bound is an improvement of the corresponding bound therein. Then, we prove a result showing how the speed on microscopic time scales affect the overall macroscopic subdiffusivity on [0, t]. Finally, we show that X moves subdiffusively even on certain microscopic time scales, in the bulk of [0, t]. The results are stated so that each gives an 'optimal survival strategy' for the system. We conclude by giving several related open problems.
DOI	10.30757/ALEA.v16-03
Cilt	16

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Subdiffusivity of brownian motion among a poissonian field of moving traps

Yazar Öz, Mehmet

Basım Tarihi 2019

Basım Yeri - Instituto Nacional de Matematica Pura e Aplicada

Konu Brownian motion in random environment, Poissonian traps, Moving trap field, Subdiffusive, Optimal survival strategy

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1980-0436

Kayıt Numarası 7ddc96f8-2747-4452-8779-08606b9f176f

Lokasyon Natural and Mathematical Sciences

Tarih 2019

Örnek Metin Our model consists of a Brownian particle X moving in N, where a Poissonian field of moving traps is present. Each trap is a ball with constant radius, centered at a trap point, and each trap point moves under a Brownian motion independently of others and of the motion of X. Here, we investigate the 'speed' of X on the time interval [0, t] and on 'microscopic' time scales given that X avoids the trap field up to time t. Firstly, following the earlier work of 'Athreya. et al. (2017), we obtain bounds on the maximal displacement of X from the origin. Our upper bound is an improvement of the corresponding bound therein. Then, we prove a result showing how the speed on microscopic time scales affect the overall macroscopic subdiffusivity on [0, t]. Finally, we show that X moves subdiffusively even on certain microscopic time scales, in the bulk of [0, t]. The results are stated so that each gives an 'optimal survival strategy' for the system. We conclude by giving several related open problems.

DOI 10.30757/ALEA.v16-03

Cilt 16