Abstract
In this paper we establish a strong decoupling inequality for the cylinder’s percolation process introduced by Tykesson and Windisch (Probab. Theory Related Fields 154 (2012) 165–191). This model features a very strong dependency structure, making it difficult to study, and this is why such decoupling inequalities are desirable. It is important to notice that the type of dependencies featured by cylinder’s percolation is particularly intricate, given that the cylinders have infinite range (unlike some models like Boolean percolation) while at the same time being rigid bodies (unlike processes such as random interlacements). Our work introduces a new notion of fast decoupling, proves that it holds for the model in question and finishes with an application. More precisely, we prove that for a small enough density of cylinders, a random walk on a connected component of the vacant set is transient for all dimensions d ≥ 3.
Original language | English |
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Pages (from-to) | 3541-3583 |
Number of pages | 43 |
Journal | Annals of Applied Probability |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2024 |
Funding
We would like to thank the two anonymous referees for a detailed reading and relevant comments that improved the exposition of the paper. This manuscript has been co-authored by UT-Battelle, LLC under Contract No. DEAC05-00OR22725 with the US Department of Energy. The United States Government retains, and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-accessplan). During this research, AT has been supported by grants \u201CProjeto Universal\u201D (406250/2016-2) and \u201CProdutividade em Pesquisa\u201D (304437/2018-2) from CNPq and \u201CJovem Cientista do Nosso Estado\u201D, (202.716/2018) from FAPERJ. CA was supported by the FAPESP grant 2013/24928, the Noise-Sensitivity Everywhere ERC Consolidator Grant 772466, and the DFG Grant SA 3465/1-1. Funding. During this research, AT has been supported by grants \u201CProjeto Universal\u201D (406250/2016-2) and \u201CProdutividade em Pesquisa\u201D (304437/2018-2) from CNPq and \u201CJovem Cientista do Nosso Estado\u201D, (202.716/2018) from FAPERJ. This manuscript has been co-authored by UT-Battelle, LLC under Contract No. DEAC05-00OR22725 with the US Department of Energy. The United States Government retains, and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-accessplan). CA was supported by the FAPESP grant 2013/24928, the Noise-Sensitivity Everywhere ERC Consolidator Grant 772466, and the DFG Grant SA 3465/1-1.
Funders | Funder number |
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United States Government | |
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro | |
U.S. Department of Energy | |
UT-Battelle | DEAC05-00OR22725 |
Fundação de Amparo à Pesquisa do Estado de São Paulo | 2013/24928 |
California Department of Fish and Game | SA 3465/1-1 |
Engineering Research Centers | 772466 |
Conselho Nacional de Desenvolvimento Científico e Tecnológico | 202.716/2018 |
DOE Public Access Plan | 406250/2016-2 |