Abstract
Abstract
We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey up to time t decays algebraically as ∼t
−θ(p,γ) where the exponent θ depends continuously on two parameters of the model, with p denoting the probability that a prey survives upon encounter with a predator and γ = D
A
/(D
A
+ D
B
) where D
A
and D
B
are the diffusion constants of the prey and the predator respectively. We also compute exactly the probability distribution P(N|t
c) of the total number of encounters till the capture time t
c and show that it exhibits an anomalous large deviation form
P
(
N
|
t
c
)
∼
t
c
−
Φ
N
ln
t
c
=
z
for large t
c. The rate function Φ(z) is computed explicitly. Numerical simulations are in excellent agreement with our analytical results.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
20 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献