### Abstract

We consider a system of independent random walks on ℤ. Let ξ_{n}(x) be the number of particles at x at time n, and let L_{n}(x)=ξ_{0}(x)+ ... +ξ_{n}(x) be the total occupation time of x by time n. In this paper we study the large deviations of L_{n}(0)-L_{n}(1). The behavior we find is much different from that of L_{n}(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when ξ_{0}(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases.

Original language | English (US) |
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Pages (from-to) | 67-82 |

Number of pages | 16 |

Journal | Probability Theory and Related Fields |

Volume | 84 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1990 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Cox, J. T., & Durrett, R. (1990). Large deviations for independent random walks.

*Probability Theory and Related Fields*,*84*(1), 67-82. https://doi.org/10.1007/BF01288559