On the first positive position of a random walker
arXiv:2501.17268 · doi:10.1007/s10955-025-03491-0
Abstract
The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of this distribution, focusing particularly on its moments and asymptotic tail behaviour, in the case where the step distribution is continuous and symmetric, encompassing both diffusive random walks and Lévy flights.
61 pages, 14 figures