A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra
A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra
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无限对称群和无限赫克代数的特征的中心极限定理
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发表时间：
2011
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通讯作者：
Pierre
中科院分区：
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作者：
Pierre
在本文中，我们回顾了无限对称群的表示理论，并通过证明无限对称群的不可约特征总是满足中心极限定理来扩展Kerov和Vershik的工作。因此，对于托马单纯形的任何点，杨氏图的水平上的相应测度具有高斯集中的属性。通过使用 Robinson-Schensted-Knuth 算法和 Pitman 算子理论，我们将这些结果与通过 riffle shuffle 获得的某些随机排列的属性以及停留在 Weyl 室中的随机游走的行为相关联。
In this paper, we review the representation theory of the infinite symmetric group, and we extend the works of Kerov and Vershik by proving that the irreducible characters of the infinite symmetric group always satisfy a central limit theorem. Hence, for any point of the Thoma simplex, the corresponding measures on the levels of the Young graph have a property of gaussian concentration. By using the Robinson-Schensted-Knuth algorithm and the theory of Pitman operators, we relate these results to the properties of certain random permutations obtained by riffle shuffles, and to the behaviour of random walks conditioned to stay in a Weyl chamber.