|Location:||MSRI: Simons Auditorium|
Abstract: We study random permutations with respect to measures that depend on the cycle structure of a permutation. The partition function for these ensembles has the general form of the Polya cycle index. Beyond the uniform case, the special case in which the measure only depends on the number of cycles (Ewens measures) has been much studied because of its relevance to modeling genetic mutations. We will present results that go beyond this case to describe typical cycle lengths as the size of permutations becomes large. This is joint work with Daniel Ueltschi.