Goncharov's Method and Its Development in the Analysis of Different Models of Random Permutations
Grigorii Ivanovich Ivchenko, Yu. I. Medvedev · Theory of Probability and Its Applications · 2003
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.