The Markov chain asymptotics of random mapping graphs

In this paper the limit behavior of random mappings with n vertices is investigated. We first compute the asymptotic probability that a fixed class of finite non-intersected subsets of vertices are located in different components and use this result to construct a scheme of allocating particles with a related Markov chain. We then prove that the limit behavior of random mappings is actually embedded in such a scheme in a certain way. As an application, we shall give the asymptotic moments of the size of the largest component.

RésuméDans cet article, nous étudions le comportement asymptotique des trasformations aléatoires à n vertex. A titre d'application nous calculons les moments asymptotiques de la taille de la plus grande composante.