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A PROBABILISTIC PROOF OF THE ROGERS–RAMANUJAN IDENTITIES

Published online by Cambridge University Press:  25 July 2001

JASON FULMAN
JASON FULMAN
Affiliation:
Stanford University Math Department, Building 380, MC 2125, Stanford, CA 94305, USA; fulman@math.stanford.edu
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Abstract

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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 4 , July 2001 , pp. 397 - 407
Copyright
© The London Mathematical Society 2001

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