On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement

In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to the expected length of each fiber. In contrast to the previously proved phase transition between sufficiently large and small fiber length, for all [Formula: see text] , FRI is NOT stochastically monotone...

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Autores principales: Cai, Zhenhao, Xiong, Yunfeng, Zhang, Yuan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7824420/
https://www.ncbi.nlm.nih.gov/pubmed/33406669
http://dx.doi.org/10.3390/e23010069
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author Cai, Zhenhao
Xiong, Yunfeng
Zhang, Yuan
author_facet Cai, Zhenhao
Xiong, Yunfeng
Zhang, Yuan
author_sort Cai, Zhenhao
collection PubMed
description In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to the expected length of each fiber. In contrast to the previously proved phase transition between sufficiently large and small fiber length, for all [Formula: see text] , FRI is NOT stochastically monotone as fiber length increases. At the same time, numerical evidence still strongly supports the existence and uniqueness of a critical fiber length, which is estimated theoretically and numerically to be an inversely proportional function with respect to system intensity.
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spelling pubmed-78244202021-02-24 On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement Cai, Zhenhao Xiong, Yunfeng Zhang, Yuan Entropy (Basel) Article In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to the expected length of each fiber. In contrast to the previously proved phase transition between sufficiently large and small fiber length, for all [Formula: see text] , FRI is NOT stochastically monotone as fiber length increases. At the same time, numerical evidence still strongly supports the existence and uniqueness of a critical fiber length, which is estimated theoretically and numerically to be an inversely proportional function with respect to system intensity. MDPI 2021-01-04 /pmc/articles/PMC7824420/ /pubmed/33406669 http://dx.doi.org/10.3390/e23010069 Text en © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Cai, Zhenhao
Xiong, Yunfeng
Zhang, Yuan
On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement
title On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement
title_full On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement
title_fullStr On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement
title_full_unstemmed On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement
title_short On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement
title_sort on (non-)monotonicity and phase diagram of finitary random interlacement
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7824420/
https://www.ncbi.nlm.nih.gov/pubmed/33406669
http://dx.doi.org/10.3390/e23010069
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