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Sharp bounds for the variance of linear statistics on random permutations
Author(s) -
Manstavičius Eugenijus
Publication year - 2020
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20951
Subject(s) - mathematics , uncorrelated , variance (accounting) , statistics , combinatorics , function (biology) , constant (computer programming) , upper and lower bounds , mathematical analysis , computer science , accounting , business , evolutionary biology , biology , programming language
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.