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Deadlock detection is an important issue in multidatabase systems. Due to the autonomy of the local systems, the visibility of the state of local transactions and the contention on item is not available. The well known PCG method exploit a weaker mean condition to detect potential global deadlock, that not necessary correspond to real one. In this paper, we present a probabilistic analysis of PCG using random graph theory and establish the foundations of a new method called Random Deadlock Detection (RDD) for which implementation and performance should be better.