Electronic Journal of Probability

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

Matías Carrasco Piaggio and Pablo Lessa

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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.

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 55, 24 pp.

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

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Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20] 28D20: Entropy and other invariants 60B05: Probability measures on topological spaces

stationary graphs Liouville property Delaunay graphs random triangulations

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Carrasco Piaggio, Matías; Lessa, Pablo. Equivalence of zero entropy and the Liouville property for stationary random graphs. Electron. J. Probab. 21 (2016), paper no. 55, 24 pp. doi:10.1214/16-EJP4650. https://projecteuclid.org/euclid.ejp/1473188082

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