  We consider a random billiard map, the one in which the standard specular
reflection rule is replaced by a random reflection given by a Markov operator.
We exhibit an invariant measure for random billiards on general tables. In the
special case of a circular table we show that almost every (random) orbit is
dense in the boundary as well as in the circular ring formed between the circle
boundary and the random caustic. We additionally prove Strong Knudsen's Law for
a particular case of families of absolutely continuous measures with respect to
Liouville.
