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arXiv · 1510.04244

Equivalence of zero entropy and the Liouville property for stationary random graphs

Matias Carrasco Piaggio·Pablo Lessa
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Abstract

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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Matias Carrasco Piaggio, Pablo Lessa. 2015-10-14. Equivalence of zero entropy and the Liouville property for stationary random graphs. https://arxiv.org/abs/1510.04244

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