### 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+σt ^{1/3}*, where parameter

*σ*controls the strength of interaction between the two groups of random walkers.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1007.1163