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We study the fundamental lower bound for node buffer size in intermittently connected wireless networks. The intermittent connectivity is caused by the possibility of node inactivity due to some external constraints. We find even with infinite channel capacity and node processing speed, buffer occupation in each node does not approach zero in a static random network where each node keeps a constant message generation rate. Given the condition that each node has the same probability p of being inactive during each time slot, there exists a critical value pc(λ) for this probability from a percolation-based perspective. When p <; pc(λ), the network is in the supercritical case, and there is an achievable lower bound (In our paper, “achievable” means that node buffer size in networks can achieve the same order as the lower bound by applying some transmission scheme) for the occupied buffer size of each node, which is asymptotically independent of the size of the network. If p > pc(λ), the network is in the subcritical case, and there is a tight lower bound Θ(√n) for buffer occupation, where n is the number of nodes in the network.