Non-intersecting, simple, symmetric random walks and the extended Hahn kernel

2004/09/01 by Kurt Johansson, Johansson, Kurt
Mathematics · #15A32 #60K35 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:15A32 #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0409013

13 pages

arxiv created 2004/09/01 · arxiv updated 2009/12/01

Abstract

Consider a particles performing simple, symmetric, non-intersecting random walks, starting at points 2(j-1), 1≤ j≤ a at time 0 and ending at 2(j-1)+c-b at time b+c. This can also be interpreted as a random rhombus tiling of an abc-hexagon, or as a random boxed planar partition confined to a rectangular box with side lengths a, b and c. The positions of the particles at all times gives a determinantal point process with a correlation kernel given in terms of the associated Hahn polynomials. In a suitable scaling limit we obtain non-intersecting Brownian motions which can be related to Dysons's Hermitian Brownian motion via a suitable transformation.

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