Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles

Details Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles

2001-07-11

arxiv.org/abs/cond-mat/0107221v2

Physics

Condensed Matter

LaTeX, 15 pages, 1 figure, minor corrections made before publication in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(01)00561-2

The vicious random walker problem on a one dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site are prohibited. It is known that the probability distribution of N walkers after M steps can be written in a determinant form. Using an integration technique borrowed from the theory of random matrices, we show that arbitrary k-th order correlation functions of the walkers can be expressed as quaternion determinants whose elements are compactly expressed in terms of symmetric Hahn polynomials.

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