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

School of Mathematical Sciences, Peking University, Beijing 100871, China
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2021, 23(1), 69; https://doi.org/10.3390/e23010069
Received: 30 November 2020 / Revised: 29 December 2020 / Accepted: 29 December 2020 / Published: 4 January 2021
(This article belongs to the Special Issue New Trends in Random Walks)
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 d3, 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. View Full-Text
Keywords: finitary random interlacement; percolation phase transition; critical value finitary random interlacement; percolation phase transition; critical value
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MDPI and ACS Style

Cai, Z.; Xiong, Y.; Zhang, Y. On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement. Entropy 2021, 23, 69. https://doi.org/10.3390/e23010069

AMA Style

Cai Z, Xiong Y, Zhang Y. On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement. Entropy. 2021; 23(1):69. https://doi.org/10.3390/e23010069

Chicago/Turabian Style

Cai, Zhenhao; Xiong, Yunfeng; Zhang, Yuan. 2021. "On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement" Entropy 23, no. 1: 69. https://doi.org/10.3390/e23010069

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