### Abstract

We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of N particles is studied and it is described by use of the probability density function of eigenvalues of [formula presented] Gaussian random matrices. The particle distribution depends on the ratio of the observation time t and the time interval T in which the nonintersecting condition is imposed. As [formula presented] is going on from 0 to 1, there occurs a transition of distribution, which is identified with the transition observed in the two-matrix model of Pandey and Mehta. Despite of the absence of matrix structure in the original vicious walker model, in the diffusion scaling limit, accumulation of contact repulsive interactions realizes the correlated distribution of eigenvalues in the multimatrix model as the particle distribution.

Original language | English |
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Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 66 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 Jul 22 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

**Scaling limit of vicious walks and two-matrix model.** / Katori, Makoto; Tanemura, Hideki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Scaling limit of vicious walks and two-matrix model

AU - Katori, Makoto

AU - Tanemura, Hideki

PY - 2002/7/22

Y1 - 2002/7/22

N2 - We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of N particles is studied and it is described by use of the probability density function of eigenvalues of [formula presented] Gaussian random matrices. The particle distribution depends on the ratio of the observation time t and the time interval T in which the nonintersecting condition is imposed. As [formula presented] is going on from 0 to 1, there occurs a transition of distribution, which is identified with the transition observed in the two-matrix model of Pandey and Mehta. Despite of the absence of matrix structure in the original vicious walker model, in the diffusion scaling limit, accumulation of contact repulsive interactions realizes the correlated distribution of eigenvalues in the multimatrix model as the particle distribution.

AB - We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of N particles is studied and it is described by use of the probability density function of eigenvalues of [formula presented] Gaussian random matrices. The particle distribution depends on the ratio of the observation time t and the time interval T in which the nonintersecting condition is imposed. As [formula presented] is going on from 0 to 1, there occurs a transition of distribution, which is identified with the transition observed in the two-matrix model of Pandey and Mehta. Despite of the absence of matrix structure in the original vicious walker model, in the diffusion scaling limit, accumulation of contact repulsive interactions realizes the correlated distribution of eigenvalues in the multimatrix model as the particle distribution.

UR - http://www.scopus.com/inward/record.url?scp=41349084951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349084951&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.66.011105

DO - 10.1103/PhysRevE.66.011105

M3 - Article

AN - SCOPUS:41349084951

VL - 66

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

ER -