UCSD MATHEMATICS DEPARTMENT: PROBABILITY SEMINAR

Random tree-automorphisms
Balint Virag, MIT
We study randomness in the automorphism group of the binary tree of depth n and its generalizations. These groups have an important role in group theory, and they also arise in connection with complex dynamics, fractals and finite automata. We use branching processes to determine the asymptotic order of a random element, answering an old question of Turan. We show that three random elements generate a large subgroup with high probability, leading to the solution of a problem of Shalev. This is joint work with M. Abert.