Dynamical correlations among vicious random walkers

Taro Nagao, Makoto Katori, Hideki Tanemura

研究成果: Article

25 引用 (Scopus)

抄録

Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin at time t = 0 and then undergo mutually avoiding Brownian motion until a finite time t = T. In the short time limit t ≪ T, the particle distribution is asymptotically described by Gaussian Unitary Ensemble (GUE) of random matrices. At the end time t = T, it is identical to that of Gaussian Orthogonal Ensemble (GOE). We show that the most general dynamical correlations among arbitrary number of particles at arbitrary number of times are written in the forms of quaternion determinants. Asymptotic forms of the correlations in the limit N → ∞ are evaluated and a discontinuous transition of the universality class from GUE to GOE is observed.

元の言語English
ページ(範囲)29-35
ページ数7
ジャーナルPhysics Letters, Section A: General, Atomic and Solid State Physics
307
発行部数1
DOI
出版物ステータスPublished - 2003 1 20
外部発表Yes

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quaternions
random walk
determinants
scaling

ASJC Scopus subject areas

  • Physics and Astronomy(all)

これを引用

Dynamical correlations among vicious random walkers. / Nagao, Taro; Katori, Makoto; Tanemura, Hideki.

:: Physics Letters, Section A: General, Atomic and Solid State Physics, 巻 307, 番号 1, 20.01.2003, p. 29-35.

研究成果: Article

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