The first positive position of a lattice random walk
Abstract
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.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Diffusion and Search Dynamics
Random Matrices and Applications
Publication details
- Journal / source
- Journal of Statistical Mechanics Theory and Experiment
- Volume
- 2026
- Issue
- 1
- Pages
- 013202–013202
- Publication date
- 1 January 2026