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arXiv · 2510.17329

The first positive position of a lattice random walk

Claude Godrèche·Jean-Marc Luck
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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.

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Claude Godrèche, Jean-Marc Luck. 2025-10-20. The first positive position of a lattice random walk. https://arxiv.org/abs/2510.17329

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