Markov chains derived from Lagrangian mechanical systems

The theory of Markov chains with countable state spaces is a greatly developed and successful area of probability theory and statistics. There is much interest in continuing to develop the theory of Markov chains beyond countable state spaces. One needs good and well motivated model systems in this effort. In this thesis, we propose to produce such systems by introducing randomness into familiar deterministic systems so that we can draw upon the existing (deterministic) results to aid the analysis of our Markov chains. We will focus most heavily on models drawn from Lagrangian mechanical systems with collisions (billiards).