THE ANNEALED SPECTRAL SAMPLE OF VORONOI PERCOLATION

• 成果类型: Article
• 署名作者: Vanneuville, Hugo
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1494
• 发表日期: 2021
• 页码: 1554-1606
• 关键词: noise sensitivity; exceptional times; probabilities

摘要

In this paper, we introduce and study the annealed spectral sample of Voronoi percolation, which is a continuous and finite point process in R-2 whose definition is mostly inspired by the spectral sample of Bernoulli percolation introduced in (Acta Math. 205 (2010) 19-104) by Garban, Pete and Schramm. We show a clustering effect as well as estimates on the full lower tail of this spectral object. Our main motivation is the study of two models of dynamical critical Voronoi percolation in the plane. In the first model, the Voronoi tiling does not evolve in time while the colors of the cells are resampled at rate 1. In the second model, the centers of the cells move according to (independent) long range stable Levy processes but the colors do not evolve in time. We prove that for these two dynamical processes there exist almost surely exceptional times with an unbounded monochromatic component.