Joint statistics of random walk on $Z^1$ and accumulation of visits
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 595-601
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We obtain the joint distribution $P_N(X,K\,|\,Z)$ of the location $X$ of a one-dimensional symmetric next neighbor random walk on the integer lattice, and the number of times the walk has visited a specified site $Z$. This distribution has a simple form in terms of the one variable distribution $p_{N'} (X')$, where $N'=N-K$ and $X'$ is a function of $X$, $K$, and $Z$. The marginal distributions of $X$ and $K$ are obtained, as well as their diffusion scaling limits.
Keywords:
symmetric random walks, walk on integer lattice, frequency of visits, walker visit number correlation.
@article{TVP_2016_61_3_a10,
author = {J. K. Percus and O. E. Percus},
title = {Joint statistics of random walk on $Z^1$ and accumulation of visits},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {595--601},
year = {2016},
volume = {61},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a10/}
}
J. K. Percus; O. E. Percus. Joint statistics of random walk on $Z^1$ and accumulation of visits. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 595-601. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a10/