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arXiv · 1605.00001

Joint Statistics of Random Walk on $Z^1$ and Accumulation of Visits

Jerome K. Percus·Ora E. Percus
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Abstract

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 distribution of $X$ and $K$ are obtained, as well as their diffusion scaling limits.

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Jerome K. Percus, Ora E. Percus. 2016-04-28. Joint Statistics of Random Walk on $Z^1$ and Accumulation of Visits. https://arxiv.org/abs/1605.00001

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