2001/11/22 by Oscar Bolina, Bolina, Oscar
Mathematics · #82B41 #FOS: Mathematics #Probability (math.PR) #Probability and Statistical Research #Stochastic processes and statistical mechanics #math.PR #msc:82B41
paper · pdf · doi:10.48550/arxiv.math/0111242
latex 8 pages, 4 figures
arxiv created 2001/11/22 · openalex publication_date 2001/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the classical one-dimensional random walk of a particle on the right-half real line. We assume that the particle is initially at position x=k, k > 0, and moves to the right with probability p or to the left with probability 1-p. We consider that the particle is absorbed at the origin without fixing the number of steps needed to get there. We calculate the probability P(x=k) that the particles end up at the origin, given that it starts at x=k, by means of a geometric representation of this random walk in terms of paths on a two-dimensional lattice.