### 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, andZ. The marginal distributions of X and K are obtained, as well as their diffusion scaling limits.

Original language | English (US) |
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Pages (from-to) | 499-505 |

Number of pages | 7 |

Journal | Theory of Probability and its Applications |

Volume | 61 |

Issue number | 3 |

DOIs | |

State | Published - 2017 |

### Keywords

- Frequency of visits
- Symmetric random walks
- Walk on integer lattice
- Walker visit number correlation

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Percus, J. K., & Percus, O. E. (2017). Joint statistics of random walk on Z

^{1}and accumulation of visits.*Theory of Probability and its Applications*,*61*(3), 499-505. https://doi.org/10.1137/S0040585X97T988307