Probability and Stochastic Analysis - University of Bonn
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Abstract of "Non-intersecting random walks in the neighborhood of a symmetric tacnode"

with Mark Adler and Pierre Van Moerbeke.

Consider a continuous time random walk in Z with independent and exponentially distributed jumps ±1. The model in this paper consists in an infinite number of such random walks starting from the complement of {-m,-m+1,...,m-1,m} at time -t, returning to the same starting positions at time t, and conditioned not to intersect. This yields a determinantal process, whose gap probabilities are given by the Fredholm determinant of a kernel. Thus this model consists of two groups of random walks, which are contained into two ellipses which, with the choice m=2t to leading order, just touch: so we have a tacnode. We determine the new limit extended kernel under the scaling m=2t+σt1/3, where parameter σ controls the strength of interaction between the two groups of random walkers.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1007.1163