Exit Probability and First Passage Time of a Lazy Pearson Walker: Scaling Behaviour

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 .