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 <inline-formula><math display="inline"...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/1/69 |
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| author | Zhenhao Cai Yunfeng Xiong Yuan Zhang |
| author_facet | Zhenhao Cai Yunfeng Xiong Yuan Zhang |
| author_sort | Zhenhao Cai |
| collection | DOAJ |
| 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 <inline-formula><math display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, 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. |
| first_indexed | 2024-03-10T13:29:54Z |
| format | Article |
| id | doaj.art-532654911d1d44b6924be10262a004af |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T13:29:54Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-532654911d1d44b6924be10262a004af2023-11-21T08:05:16ZengMDPI AGEntropy1099-43002021-01-012316910.3390/e23010069On (Non-)Monotonicity and Phase Diagram of Finitary Random InterlacementZhenhao Cai0Yunfeng Xiong1Yuan Zhang2School of Mathematical Sciences, Peking University, Beijing 100871, ChinaSchool of Mathematical Sciences, Peking University, Beijing 100871, ChinaSchool of Mathematical Sciences, Peking University, Beijing 100871, ChinaIn 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 <inline-formula><math display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, 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.https://www.mdpi.com/1099-4300/23/1/69finitary random interlacementpercolation phase transitioncritical value |
| spellingShingle | Zhenhao Cai Yunfeng Xiong Yuan Zhang On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement Entropy finitary random interlacement percolation phase transition critical value |
| 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 | finitary random interlacement percolation phase transition critical value |
| url | https://www.mdpi.com/1099-4300/23/1/69 |
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