TITLE:
Exit Probability and First Passage Time of a Lazy Pearson Walker: Scaling Behaviour
AUTHORS:
Muktish Acharyya
KEYWORDS:
Pearson Walker, Lazy Random Walk, Exit Probability, First Passage Time, Scaling
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.12,
July
27,
2016
ABSTRACT: The motion of a lazy Pearson walker is
studied with different probability (p) of jump in two and three dimensions. The
probability of exit ( ) from a zone of radius is studied as a function of with
different values of jump probability p. The exit probability is found to scale
as , which is obtained by method of data collapse. The first passage time ( )
i.e., the time required for first exit from a zone is studied. The probability
distribution of first passage time was studied for different values of jump probability
(p). The probability distribution of first passage time was found to scale as .
Where, F and G are two scaling functions and a, b, g and d are some
exponents. In both the dimensions, it is found that, , , and .