Distributed consensus and linear functional calculation in networks: an observability perspective
Proceedings of the 6th international conference on Information processing in sensor networks
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Let A be an n 脳 n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^{-1} does not exceed Cn^{3/2} with probability close to 1. In a geometric language, this bounds the probability that the affine span of n random vectors in \mathbb{R}^n with i.i.d. subgaussian coordinates comes close to the origin.