Ce rapport présente une étude qui établit une relation probabiliste entre la taille d'un noyau dans un système pair-à-pair et le période au bout de la quelle un nouveau noyau \ Distributed systems are now both very large and highly dynamic. Peer to peer overlay networks have proven efficient to cope with this new deal that traditional approaches can no longer accommodate. While organizing peers in an overlay network have generated a lot of interest leading to a large number of solutions, maintaining critical data in such a network remains an open issue. In this paper, we are interested in defining the portion of nodes and frequency one has to probe, given the churn observed in the system in order to achieve a given probability of maintaining the persistence of some critical data. More specifically, we provide a clear result relating the size and the frequency of the probing set along with its proof as well as an analysis of the way of leveraging such an information in a large scale dynamic distributed system.
