A Central Limit Theorem for the Thompson Group $F$

Arundhathi Krishnan (Munster Technological University)

Thursday 18th May 16:00-17:00 Maths 311B


We discuss a central limit theorem in the framework of the Thompson group $F$. For this purpose, we consider the standard infinite presentation of the group $F$ and denote the generators of $F$ by $g_n$. We show that the large-$n$ limit law of the self-adjoint element $s_n = \frac{1}{\sqrt{2n}}(g_0 + g_{0}^{-1} + ... + g_{n-1} + g_{n-1}^{-1} )$ (with respect to the left regular trace as expectation functional) is a centered normal distribution.  Our proof combines standard combinatorial arguments for algebraic central limit theorems and abstract reduction system techniques, as deployed by Dehornoy in the study of the Thompson group $F$.  

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