The first positive position of a lattice random walk
Statistical Mechanics
2025-10-21 v1 Probability
Abstract
The distribution of the first positive position reached by a random walker starting at the origin is central to the analysis of extremes and records in one-dimensional random walks. In this work, we present a detailed and self-contained analytical study of this distribution for symmetric finite-range lattice walks, whose steps are drawn from a distribution supported on finitely many integers.
Cite
@article{arxiv.2510.17329,
title = {The first positive position of a lattice random walk},
author = {Claude Godrèche and Jean-Marc Luck},
journal= {arXiv preprint arXiv:2510.17329},
year = {2025}
}
Comments
25 pages, 3 figures