### 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 2003 |

### Fingerprint

### Keywords

- Brownian walkers
- Diffusion-limited reactions
- Voter model

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

**Statistical Description of Contact-Interacting Brownian Walkers on the Line.** / Fatkullin, Ibrahim; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 112, no. 1-2, pp. 155-163. https://doi.org/10.1023/A:1023627604000

}

TY - JOUR

T1 - Statistical Description of Contact-Interacting Brownian Walkers on the Line

AU - Fatkullin, Ibrahim

AU - Vanden Eijnden, Eric

PY - 2003/7

Y1 - 2003/7

N2 - 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.

AB - 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.

KW - Brownian walkers

KW - Diffusion-limited reactions

KW - Voter model

UR - http://www.scopus.com/inward/record.url?scp=0037727563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037727563&partnerID=8YFLogxK

U2 - 10.1023/A:1023627604000

DO - 10.1023/A:1023627604000

M3 - Article

AN - SCOPUS:0037727563

VL - 112

SP - 155

EP - 163

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -