  Consider a continuous time random walk in $\mathbb{Z}$ with independent and
exponentially distributed jumps $\pm1$. The model in this paper consists in an
infinite number of such random walks starting from the complement of
$\{-m,-m+1,\ldots,m-1,m\}$ 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 $m\simeq2t$ to leading
order, just touch: so we have a tacnode. We determine the new limit extended
kernel under the scaling $m=\lfloor2t+\sigma t^{1/3}\rfloor$, where parameter
$\sigma$ controls the strength of interaction between the two groups of random
walkers.
