Equivalence of zero entropy and the Liouville property for stationary random graphs
classification
🧮 math.PR
keywords
randomentropygraphsinfinitestationaryadmitsalmostapplications
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We prove that any stationary random graph satisfying a growth condition and having positive entropy almost surely admits an infinite dimensional space of bounded harmonic functions. Applications to random infinite planar triangulations and Delaunay graphs are given.
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