Vicious Walkers and Hook Young Tableaux
Statistical Mechanics
2009-11-07 v2 Probability
Exactly Solvable and Integrable Systems
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 walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.
Keywords
Cite
@article{arxiv.cond-mat/0209512,
title = {Vicious Walkers and Hook Young Tableaux},
author = {Kazuhiro Hikami and Takashi Imamura},
journal= {arXiv preprint arXiv:cond-mat/0209512},
year = {2009}
}
Comments
23 pages, 5 figures