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2016 Equivalence of zero entropy and the Liouville property for stationary random graphs
Matías Carrasco Piaggio, Pablo Lessa
Electron. J. Probab. 21: 1-24 (2016). DOI: 10.1214/16-EJP4650

Abstract

We prove that any rooted 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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Matías Carrasco Piaggio. Pablo Lessa. "Equivalence of zero entropy and the Liouville property for stationary random graphs." Electron. J. Probab. 21 1 - 24, 2016. https://doi.org/10.1214/16-EJP4650

Information

Received: 20 October 2015; Accepted: 1 August 2016; Published: 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1346.05276
MathSciNet: MR3546392
Digital Object Identifier: 10.1214/16-EJP4650

Subjects:
Primary: 05C80 , 28D20 , 60B05

Keywords: Delaunay graphs , Liouville property , random triangulations , stationary graphs

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