The plancherel measure for symmetric graphs
نویسندگان
چکیده
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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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 function...
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1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...
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This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...
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A partition of a natural number n is any integer sequence λ = (λ1, λ2, . . . ) such that λ1 ≥ λ2 ≥ · · · ≥ 0 and λ1 + λ2 + · · · = n (notation: λ ⊢ n). In particular, λ1 = max{λi ∈ λ}. Every partition λ ⊢ n can be represented geometrically by a planar shape called the Young diagram, consisting of n unit cell arranged in consecutive columns, containing λ1, λ2, . . . cells, respectively. On the s...
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ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata
سال: 1984
ISSN: 0373-3114,1618-1891
DOI: 10.1007/bf01762541