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