Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks

Abstract

We derive an asymptotic expansion for the subgroup of arbitrary Fuchsian groups and some other classes of large groups. Moreover, the main conjecture for Random Walks on symmetric groups is established in full generality. Both problems require subtle estimates of character values and root number multiplicities for symmetric groups, which are also of independent interest.

57 pages, submitted to Acta Mathematica