  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.
