We are concerned with the variance of a completely additive function defined on the symmetric group endowed with the Ewens probability. Overcoming specific dependence of the summands, we obtain the upper and lower bounds including optimal constants. We also derive a decomposition of such a function into a sum with uncorrelated summands. The results can be reformulated for the linear statistics defined on vectors distributed according to the Ewens sampling formula.

中文翻译：

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随机排列的线性统计量的方差的鲜明边界

我们关注的是在赋予Ewens概率的对称群上定义的完全加法函数的方差。克服求和数的特定依赖关系，我们获得了包括最佳常数的上下限。我们还将这种函数分解为具有不相关求和数的和。可以针对根据Ewens采样公式分布的向量上定义的线性统计重新计算结果。