2018/06/21 by Hugo Vanneuville, Vanneuville, Hugo
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1806.08452
openalex publication_date 2018/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.