Annealed scaling relations for Voronoi percolation

Hugo Vanneuville

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arXiv · 1806.08452

Annealed scaling relations for Voronoi percolation

Hugo Vanneuville

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Abstract

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 [Kes87]. 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 [AGMT16]. Intermediate results also include the study of quenched and annealed notions of pivotal events and the extension of the quenched box-crossing property of [AGMT16] to the near-critical regime.

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Hugo Vanneuville. 2018-06-21. Annealed scaling relations for Voronoi percolation. https://arxiv.org/abs/1806.08452

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