Author
Öz, Mehmet
Publication Date
2019
Publication Place
-
Instituto Nacional de Matematica Pura e Aplicada
Subject
Brownian motion in random environment, Poissonian traps, Moving trap field, Subdiffusive, Optimal survival strategy
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1980-0436
Record ID
7ddc96f8-2747-4452-8779-08606b9f176f
Library Location
Natural and Mathematical Sciences
Date
2019
Sample Text
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
