On a variance related to the Ewens sampling formula
Eugenijus Manstavičius
Vilnius University, Lithuania
Žydrūnas Žilinskas
Vilnius University, Lithuania
Published 2011-12-07


random permutation
cycle structure
integral operator
matrix eigenvalue
Jacobi polynomial

How to Cite

Manstavičius E. and Žilinskas Žydrūnas (2011) “On a variance related to the Ewens sampling formula”, Nonlinear Analysis: Modelling and Control, 16(4), pp. 453-466. doi: 10.15388/NA.16.4.14088.


A one-parameter multivariate distribution, called the Ewens sampling formula, was introduced in 1972 to model the mutation phenomenon in genetics. The case discussed in this note goes back to Lynch’s theorem in the random binary search tree theory. We examine an additive statistics, being a sum of dependent random variables, and find an upper bound of its variance in terms of the sum of variances of summands. The asymptotically best constant in this estimate is established as the dimension increases. The approach is based on approximation of the extremal eigenvalues of appropriate integral operators and matrices.

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