Asymptotics for conjugacy classes of free groups

George Kenison (University of Warwick)

Frank Adams 1,

Let \(G\) be a finite connected metric graph such that the degree of each vertex is at least 3.  The fundamental group of \(G\) is a free group \(F\) and the universal cover of \(G\) is a tree \(\mathcal{T}\). We are interested in asymptotics related to the action of \(F\) on \(\mathcal{T}\); in particular, when the elements of \(F\) are restricted to a non-trivial conjugacy class.  Time permitting, we will discuss two results: an equidistribution limit and a central limit asymptotic.  This is joint work with Richard Sharp.

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