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UCSD MATHEMATICS DEPARTMENT: PROBABILITY SEMINAR
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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.