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Distribution of the First Hitting Point on a Boundary Set for a Random Walk in a Lattice Strip
Abstract
We consider a time-homogeneous random walk in a strip of a two-dimensional lattice whose transition probabilities are invariant under shifts along one of the coordinates. We study the limiting distribution of the first hitting point into a boundary set as the initial condition tends to infinity. Explicit expressions are obtained for this limiting distribution for negative and zero mean drift.
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BibTeX
@misc{kuzin2026distribution,
title = {{Distribution of the First Hitting Point on a Boundary Set for a Random Walk in a Lattice Strip}},
author = {I. M. Kuzin and A. A. Zamyatin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35406},
eprint = {2610.35406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35406},
}
RIS
TY - UNPB
TI - Distribution of the First Hitting Point on a Boundary Set for a Random Walk in a Lattice Strip
AU - I. M. Kuzin
AU - A. A. Zamyatin
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35406
UR - https://arxiv.org/abs/2610.35406
AB - We consider a time-homogeneous random walk in a strip of a two-dimensional lattice whose transition probabilities are invariant under shifts along one of the coordinates. We study the limiting distribution of the first hitting point into a boundary set as the initial condition tends to infinity. Explicit expressions are obtained for this limiting distribution for negative and zero mean drift.
ER -