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Assuming a series of random geometric graph G1,G2,...,Gn. For each Gi, |V|=N, and nodes are distributed as a possion point process. If the distance between a pair of nodes is less than or equal to r, there is an edge between them. The corresponding adjacent matrix of Gi is Ai. What is the result of A1*A2*...*An?

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Zero, with a probability increasing with $n$. –  Carl Jul 17 '13 at 12:22
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