Vicious walkers and hook Young tableaux

Authors: Hikami K.; Imamura T.

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3033-3048(16)

Publisher: Institute of Physics Publishing

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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.

Language: English

Document Type: Miscellaneous

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