Abstract: In the mathematical physics literature there existe a huge amount of work on point interactions. Some years ago Mueller and Fleischmann demonstrated that it is in principle possible to study point interactions from a probabilistic perspective. They constructed a stochastic process such that the expectation of certain functionals solves the heat equation with a single point source. An understanding of even the most basic properties of this process is still missing. In the talk the result of Fleischmann and Mueller will be described, some heuristic explanations will be given and some results concerning the large time behavior will be presented.