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.