We examine the variance of a linear statistic defined on the symmetric group endowed with the Ewens probability. Despite the dependence of the summands, it can be bounded from above by a constant multiple of the sum of variances of the summands. We find the exact value of this constant. The analysis of the appearing quadratic forms and eigenvalue search is built upon the exponential matrices and discrete Hahn’s polynomials.

中文翻译：

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关于 Ewens 抽样公式的方差的急剧不等式

我们检查在赋予 Ewens 概率的对称组上定义的线性统计量的方差。尽管有被加数的依赖性，但它可以由被加数的方差总和的常数倍数从上方限定。我们找到了这个常数的确切值。对出现的二次形式和特征值搜索的分析建立在指数矩阵和离散哈恩多项式的基础上。