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A Representation for non-colliding random walks

O'Connell, Neil; Yor, Marc

HPL-BRIMS-2001-04R1

Keyword(s): GUE; eigenvalues of random matrices; Hermitian Brownian motion; non-colliding Brownian motions; Weyl chamber; queues in series; Burke's theorem; reversibility; Pitman's representation theorem; Charlier ensemble

Abstract: We obtain a representation for non-colliding (one- dimensional, one-sided) random walks as a functional of the same number of independent walks. This can be regarded as a multi-dimensional generalisation of Pitman's representation for the three-dimensional Bessel process. Notes: Marc Yor, Laboratoire de Probabilites, Universite Pierre et Marie Curie, 4 Place Jussieu F-75252 Paris Cedex 05, France.

14 Pages

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