Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3033-3048 |
| Number of pages | 16 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 36 |
| Issue number | 12 SPEC. ISS. |
| DOIs | |
| Publication status | Published - Mar 28 2003 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
Cite this
Vicious walkers and hook Young tableaux. / Hikami, Kazuhiro; Imamura, Takashi.
In: Journal of Physics A: Mathematical and General, Vol. 36, No. 12 SPEC. ISS., 28.03.2003, p. 3033-3048.Research output: Contribution to journal › Article
}
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.
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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 -