Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burnside and Brauer on the decomposition of tensor products.
The central limit theorem for extremal characters of the infinite symmetric group
Second cohomology for finite groups of Lie type
On $τ$-tilting finiteness of block algebras of direct products of finite groups
![QR code for arXiv:math/0402409 [math.RT]](http://oss.arxitics.com/images/favicon.svg)