Stein's Method and Plancherel Measure of the Symmetric Group
نویسنده
چکیده
We initiate a Stein’s method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov’s central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the proof gives an error term. The construction of an exchangeable pair needed for applying Stein’s method arises from the theory of harmonic functions on Bratelli diagrams. We also find the spectrum of the Markov chain on partitions underlying the construction of the exchangeable pair. This yields an intriguing method for studying the asymptotic decomposition of tensor powers of some representations of the symmetric group.
منابع مشابه
Stein's Method and Plancherel Measure of the Symmetric Group Running Head: Stein's Method and Plancherel Measure
X iv :m at h/ 03 05 42 3v 3 [ m at h. R T ] 1 1 N ov 2 00 3 Stein’s Method and Plancherel Measure of the Symmetric Group Running head: Stein’s Method and Plancherel Measure By Jason Fulman University of Pittsburgh Department of Mathematics 301 Thackeray Hall Pittsburgh, PA 15260 Email: [email protected] Abstract: We initiate a Stein’s method approach to the study of the Plancherel measure of...
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