The expected time until opinions on an n-vertex graph differ by at most ε is Õ(n^{max(3-p,2/p)}) when each initial opinion has L^p norm at most 1, and this scaling is tight on cycles.
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Edge-averaging dynamics on finite graphs: moment dependence
The expected time until opinions on an n-vertex graph differ by at most ε is Õ(n^{max(3-p,2/p)}) when each initial opinion has L^p norm at most 1, and this scaling is tight on cycles.