### Abstract

The distribution of interval lengths between Brownian walkers on the line is investigated. The walkers are independent until collision; at collision, the left walker disappears, and the right walker survives with probability p. This problem arises in the context of diffusion-limited reactions and also in the scaling limit of the voter model. A systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths. The first approximation beyond mere statistical independence between successive intervals already gives excellent results, as established by comparison with direct numerical simulations.

Original language | English (US) |
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Pages (from-to) | 155-163 |

Number of pages | 9 |

Journal | Journal of Statistical Physics |

Volume | 112 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1 2003 |

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### Keywords

- Brownian walkers
- Diffusion-limited reactions
- Voter model

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*112*(1-2), 155-163. https://doi.org/10.1023/A:1023627604000