Sharp bounds for the variance of linear statistics on random permutations. Issue 4 (20th July 2020)

• Record Type: Journal Article
• Authors: Manstavičius, Eugenijus
• Is Part Of: Random structures & algorithms. Volume 57:Issue 4(2020)
• Page Start: 1303
• Page End: 1313
• Publication Date: 2020-07-20
• Subjects: discrete Hahn's polynomials -- Ewens sampling formula -- symmetric group -- Turán‐Kubilius inequality; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20951
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : 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.