Nonintersecting random walks in the neighborhood of a symmetric tacnode

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.2t to leading order, just touch: so we have a tacnode. We determine the new limit extended kernel under the scaling m=.2t+.t1/3., where parameter . controls the strength of interaction between the two groups of random walkers.