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In this paper, we focus on enhancing the data accessibility of ad hoc networks, with emphasis on peer-to-peer communications. To achieve this goal, we propose a randomized distributed algorithm for data replication. Furthermore, a probabilistic approach is presented to derive the upper bound of convergence by a novel technique, called path coupling, which gives more insight into factors determining system performance. Our analysis demonstrates that data accessibility can be improved by the proposed approach, with very limited memory consumption.