## Discrete Random Walks, DRW'03

### Cyril Banderier and Christian Krattenthaler (eds.)

### DMTCS Conference Volume AC (2003), pp. 83-94

author: | Michael Drmota |
---|---|

title: | Discrete Random Walks on One-Sided ``Periodic'' Graphs |

keywords: | discrete random walk, generating functions, singularity analysis |

abstract: | In this paper we consider discrete random walks on infinite graphs that are generated by copying and shifting one finite (strongly connected) graph into one direction and connecting successive copies always in the same way. With help of generating functions it is shown that there are only three types for the asymptotic behaviour of the random walk. It either converges to the stationary distribution or it can be approximated in terms of a reflected Brownian motion or by a Brownian motion. In terms of Markov chains these cases correspond to positive recurrence, to null recurrence, and to non recurrence. |

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reference: | Michael Drmota (2003), Discrete
Random Walks on One-Sided ``Periodic'' Graphs, in
Discrete Random Walks, DRW'03, Cyril Banderier and
Christian Krattenthaler (eds.), Discrete Mathematics and
Theoretical Computer Science Proceedings AC, pp.
83-94 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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