2015/05/31 by Ajanta Bhowal Acharyya, Acharyya, Ajanta Bhowal
Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1506.00269
7 Pages text (Latex) + 9 Latex figures
arxiv created 2015/06/05 · arxiv updated 2015/06/08
We are studying the motion of a random walker in two and three dimensional continuum with uniformly distributed jump-length. This is different from conventional Lavy flight. In 2D and 3D continuum, a random walker can move in any direction, with equal probability and with any step-length(l) varying randomly between 0 to 1 with equal probability. A random walker, who starts his journey from a particular point (taken as origin), walks through the region, centered around the origin. Here, in this paper, we studied the probability distribution of end-to-end distances and the probability of return for the first time within a circular zone of finite radius, centered about the initial point, of a random walker. We also studied the same when a random walker moves with constant step-length, unity. The probability distribution of the time of first return (within a specified zone) is also studied.