Dynamical correlations among vicious random walkers 

作成者 香取, 眞理, 永尾, 太郎, 種村, 秀紀
作成者 (ヨミ) タネムラ, ヒデキ
作成者の別表記 Katori, Makoto, Nagao, Taro, Tanemura, Hideki
キーワード等 Vicious random walk, Random matrices
日本十進分類法 (NDC) 421.5
内容 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.
コンテンツの種類 雑誌掲載論文 Journal Article
DCMI資源タイプ text
ファイル形式 application/x-dvi
DOI 10.1016/S0375-9601(02)01661-4
掲載誌情報 Physics letters. Sect. A Vol.307 no.1 page.29-35 (2003)
言語 英語
関連情報 (hasVersion)
著者版フラグ author

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Random matrices