Random Matrices From GLn(q) Sampled by Words

Doron Puder studies probability distributions on finite groups obtained by evaluating a free-group word on uniformly random group elements. Earlier work connected such distributions on symmetric groups with the partially ordered set of finitely generated free-group subgroups. The talk introduces free groups and free-group algebras, then develops new connections between word distributions on matrix groups over finite fields and free-group algebras. It compares these findings with the symmetric-group case and presents related conjectures. Joint work with Danielle Ernst-West and Matan Seidel.