Open Access
2019 Annealed scaling relations for Voronoi percolation
Hugo Vanneuville
Electron. J. Probab. 24: 1-71 (2019). DOI: 10.1214/19-EJP293


We prove annealed scaling relations for planar Voronoi percolation. To our knowledge, this is the first result of this kind for a continuum percolation model. We are mostly inspired by the proof of scaling relations for Bernoulli percolation by Kesten [22]. Along the way, we show an annealed quasi-multiplicativity property by relying on the quenched box-crossing property proved by Ahlberg, Griffiths, Morris and Tassion [3]. Intermediate results also include the study of quenched and annealed notions of pivotal events and the extension of the quenched box-crossing property of [3] to the near-critical regime.


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Hugo Vanneuville. "Annealed scaling relations for Voronoi percolation." Electron. J. Probab. 24 1 - 71, 2019.


Received: 24 July 2018; Accepted: 17 March 2019; Published: 2019
First available in Project Euclid: 10 April 2019

zbMATH: 07055677
MathSciNet: MR3940769
Digital Object Identifier: 10.1214/19-EJP293

Primary: 60K35 , 60K37

Keywords: Near-criticality , percolation , quasi-multiplicativity , random environment , scaling relation , Voronoi tiling

Vol.24 • 2019
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