Quantitative quenched Voronoi percolation and applications
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| Názov: | Quantitative quenched Voronoi percolation and applications |
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| Autori: | Vanneuville, Hugo |
| Prispievatelia: | Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Probabilités, statistique, physique mathématique (PSPM), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL) |
| Zdroj: | To be published in AIHP |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Cellule MathDoc/Centre Mersenne, 2025. |
| Rok vydania: | 2025 |
| Predmety: | [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Probability (math.PR), FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), 0101 mathematics, 01 natural sciences, Mathematics - Probability, Mathematical Physics |
| Popis: | Ahlberg, Griffiths, Morris and Tassion have proved that, asymptotically almost surely, the quenched crossing probabilities for critical planar Voronoi percolation do not depend on the environment. We prove an analogous result for arm events. In particular, we prove that the variance of the quenched probability of an arm event is at most a constant times the square of the annealed probability. The fact that the arm events are degenerate and non-monotonic add two major difficulties. As an application, we prove that there exists ϵ>0 such that the following holds for the annealed percolation function θ an :∀p>1/2,θ an (p)≥ϵ(p-1/2) 1-ϵ .One of our motivations is to provide tools for a spectral study of Voronoi percolation. |
| Druh dokumentu: | Article Other literature type Report |
| Jazyk: | English |
| ISSN: | 1777-5310 |
| DOI: | 10.5802/aif.3710 |
| DOI: | 10.48550/arxiv.1806.08448 |
| Prístupová URL adresa: | http://arxiv.org/abs/1806.08448 |
| Rights: | arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....6563f4c3fe20d5e33e119fc1aeee261d |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Ahlberg, Griffiths, Morris and Tassion have proved that, asymptotically almost surely, the quenched crossing probabilities for critical planar Voronoi percolation do not depend on the environment. We prove an analogous result for arm events. In particular, we prove that the variance of the quenched probability of an arm event is at most a constant times the square of the annealed probability. The fact that the arm events are degenerate and non-monotonic add two major difficulties. As an application, we prove that there exists ϵ>0 such that the following holds for the annealed percolation function θ an :∀p>1/2,θ an (p)≥ϵ(p-1/2) 1-ϵ .One of our motivations is to provide tools for a spectral study of Voronoi percolation. |
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| ISSN: | 17775310 |
| DOI: | 10.5802/aif.3710 |