Abstract
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 within two ellipses which, with the choice m similar or equal to 2t to leading order, just touch: so we have a tacnode. We determine the new limit extended kernel under the scaling m = left perpendicular2t +sigma t(1/3)right perpendicular, where parameter sigma controls the strength of interaction between the two groups of random walkers.