A probabilistic proof of the Rogers-Ramanujan identities

The asymptotic probability theory of conjugacy classes of the finite general groups leads to a probability measure on the set of all partitions of natural numbers. A simple method of understanding these measures in terms of Markov chains is given in this paper, leading to an elementary probabilistic proof of the Rogers-Ramanujan identities. This is compared with work on the uniform measure. The main case of Bailey's lemma is interpreted as finding eigenvectors of the transition matrix of a Markov chain. It is shown that the viewpoint of Markov chains extends to quivers.