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Advances in VLSI technology and communication devices make possible low-power wireless sensor networks. Due to power limitations or dependence only on ambient energy sources, we propose a "stochastic" sensor network, in which each node may be active asynchronously for only a fraction of the time. Networking functions are accomplished by stochastic flooding. We determine the operating regime, namely that N·PA>1, in which such a network is quasistable, so that the lifetime of the transmitted message is large and the message reaches its intended destination with high probability. The analysis shows the network is capable of supporting unicast and multicast communication, as well as active networking.