Brownian motion is both a Gaussian and a Markov process. Nevertheless,
until ten years ago, these specializations in the field of stochastic
processes where considered very different and had hardly any common
practitioners. Then Dynkin obtained a startling and difficult, isomorphism
theorem relating the local times of symmetric Markov processes to certain
associated Gaussian processes. Jay Rosen and I have been exploring this
relationship since then. Recently we have simplified Dynkins approach to
the point where we can obtain many results about the local times
of symmetric Markov processes in general and Ray-Knight theorems for
diffusions using little more than elementary linear algebra. I will survey
some of our results in a lecture prepared for a general mathematical audience.