Vicious Walkers and Hook Young Tableaux

Kazuhiro Hikami, Takashi Imamura

Published 2002-09-23, updated 2003-03-14Version 2

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.