Fluctuation Theory for the Ehrenfest urn

The Ehrenfest urn model with d balls, or alternatively random walk on the unit cube in d dimensions, is considered in discrete and continuous time, together with related models. Attention is focused on the fluctuation theory of the model.behaviour on unusual states.and in particular on first passage to the opposite vertex. Applications to statistical mechanics, reliability theory and genetics are surveyed, and some new results are obtained.