A Sharp Bound on the s-Energy.
arXiv: Multiagent Systems(2018)
摘要
We derive an (essentially) optimal bound of $O(1/rho s)^{n-1}$ on the $s$-energy of an $n$-agent averaging system, where $rho$ 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.
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