A Sharp Bound on the s-Energy

02/04/2018

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by   Bernard Chazelle, et al.

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We derive an (essentially) optimal bound of O(1/ρ s)^n-1 on the s-energy of an n-agent averaging system, where ρ is a lower bound on the nonzero weights. The s-energy is a generating function with applications to opinion dynamics, synchronization, consensus, bird flocking, inhomogeneous products of stochastic matrices, etc. We discuss a few of the improvements one can derive from the new bounds.