A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal Groups

Abstract

Markov chains are used to give a purely probabilistic way of understanding the conjugacy classes of the finite symplectic and orthogonal groups in odd characteristic. As a corollary of these methods one obtains a probabilistic proof of Steinberg's count of unipotent matrices and generalizations of formulas of Rudvalis and Shinoda.

Revised version; to appear in J. Algebra. Same results. We fix a possibly misleading typo, replacing u by u^2 in some normalization constants