抄録
We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of movements of the walker. Applying the saddle point method, we reveal that the scaling limit gives the Tracy-Widom distribution, which is the same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.
| 元の言語 | 英語 |
|---|---|
| ページ（範囲） | 3033-3048 |
| ページ数 | 16 |
| ジャーナル | Journal of Physics A: Mathematical and General |
| 巻 | 36 |
| 発行部数 | 12 SPEC. ISS. |
| DOI | |
| 出版物ステータス | 出版済み - 3 28 2003 |
| 外部発表 | Yes |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
これを引用
Vicious walkers and hook Young tableaux. / Hikami, Kazuhiro; Imamura, Takashi.
：: Journal of Physics A: Mathematical and General, 巻 36, 番号 12 SPEC. ISS., 28.03.2003, p. 3033-3048.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - Vicious walkers and hook Young tableaux
AU - Hikami, Kazuhiro
AU - Imamura, Takashi
PY - 2003/3/28
Y1 - 2003/3/28
N2 - We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of movements of the walker. Applying the saddle point method, we reveal that the scaling limit gives the Tracy-Widom distribution, which is the same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.
AB - We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of movements of the walker. Applying the saddle point method, we reveal that the scaling limit gives the Tracy-Widom distribution, which is the same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.
UR - http://www.scopus.com/inward/record.url?scp=0037471251&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037471251&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/36/12/311
DO - 10.1088/0305-4470/36/12/311
M3 - Article
VL - 36
SP - 3033
EP - 3048
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 12 SPEC. ISS.
ER -