A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group

@inproceedings{Hora2003ANV,
  title={A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group},
  author={Akihito Hora},
  year={2003}
}
We give a noncommutative extension of Kerov’s central limit theorem for irreducible characters of the symmetric group with respect to the Plancherel measure [S.Kerov:C.R.Acad.Sci.Paris 316 (1993)]in the framework of algebraic probability theory.For adjacency operators associated with the cycle classes, we consider their decomposition according to the length function on the Cayley graph of the symmetric group.We develop a certain noncommutative central limit theorem for them, in which the limit… CONTINUE READING

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