This article is cited in 12 papers

Short Communications

Goncharov's method and its development in the analysis of different models of random permutations

G. I. Ivchenko, Yu. I. Medvedev

Moscow State Institute of Electronics and Mathematics

Abstract: We show the efficiency of the generating functions method first used by Goncharov who analyzed asymptotic properties of random permutations in a problem of investigating joint distributions of maximal cycle lengths of a random permutation in the Ewens model. The explicit form of the respective multidimensional Goncharov density and its generalizations are obtained.

Keywords: random permutation, random polynomial over finite field, generating function, limit theorem.

Received: 01.10.2001

DOI: 10.4213/tvp3695

 English version: Theory of Probability and its Applications, 2003, 47:3, 518–526

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