Let $S_n$, $n\in\bold N$, be a recurrent random walk on ${\bold Z}^2$ $(S_0=0)$ and let $\xi(\alpha)$, $\alpha\in{\bold Z}^2$, be i.i.d. $\bold R$-valued centered random variables. It is shown that $\sum^n_{i=1}\xi(S_i)/ \sqrt{n\log n}$ satisfies a central limit theorem. A functional version is also presented.

Bolthausen, E (1989). *A central limit theorem for two-dimensional random walks in random sceneries.* The Annals of Probability, 17(1):108-115.

## Abstract

Let $S_n$, $n\in\bold N$, be a recurrent random walk on ${\bold Z}^2$ $(S_0=0)$ and let $\xi(\alpha)$, $\alpha\in{\bold Z}^2$, be i.i.d. $\bold R$-valued centered random variables. It is shown that $\sum^n_{i=1}\xi(S_i)/ \sqrt{n\log n}$ satisfies a central limit theorem. A functional version is also presented.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | Random walk; random scenery; central limit theorem |

Language: | English |

Date: | 1989 |

Deposited On: | 21 May 2010 08:11 |

Last Modified: | 05 Apr 2016 13:29 |

Publisher: | Institute of Mathematical Statistics |

ISSN: | 0091-1798 |

Publisher DOI: | https://doi.org/10.1214/aop/1176991497 |

Related URLs: | http://www.zentralblatt-math.org/zmath/en/search/?q=an:0679.60028 |

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