Long cycle of random permutations with polynomially growing cycle weights. Issue 4 (22nd December 2020) - Zeindler, Dirk
Abstract : We study random permutations of n objects with respect to multiplicative measures with polynomial growing cycle weights. We determine in this paper the asymptotic behavior of the long cycles under this measure and also prove that the cumulative cycle numbers converge in the region of the long cycles to a Poisson process.