Vicious walkers and hook Young tableaux

Kazuhiro Hikami; Takashi Imamura

doi:10.1088/0305-4470/36/12/311

Vicious walkers and hook Young tableaux

Kazuhiro Hikami, Takashi Imamura

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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	https://doi.org/10.1088/0305-4470/36/12/311
Publication status	Published - Mar 28 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/36/12/311

Cite this

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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.",

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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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DO - 10.1088/0305-4470/36/12/311

M3 - Article

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JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 12 SPEC. ISS.

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Vicious walkers and hook Young tableaux

Abstract

All Science Journal Classification (ASJC) codes

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