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Critical exponents for a percolation model on transient graphs

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Main Authors: Alexander, Drewitz, Alexis, Prévost, Pierre-François, Rodriguez
Format: Book
Language:English
Published: 2023
Subjects:
(near-)critical regime
three-dimensional cubic lattice
Online Access:https://link.springer.com/article/10.1007/s00222-022-01168-z
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7416
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spelling oai:localhost:PNK-74162023-04-03T03:35:42Z Critical exponents for a percolation model on transient graphs Alexander, Drewitz Alexis, Prévost Pierre-François, Rodriguez (near-)critical regime three-dimensional cubic lattice CC BY We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the values of the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension. 2023-04-03T02:58:16Z 2023-04-03T02:58:16Z 2022 Book https://link.springer.com/article/10.1007/s00222-022-01168-z https://dlib.phenikaa-uni.edu.vn/handle/PNK/7416 en application/pdf
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic (near-)critical regime
three-dimensional cubic lattice
spellingShingle (near-)critical regime
three-dimensional cubic lattice
Alexander, Drewitz
Alexis, Prévost
Pierre-François, Rodriguez
Critical exponents for a percolation model on transient graphs
description CC BY
format Book
author Alexander, Drewitz
Alexis, Prévost
Pierre-François, Rodriguez
author_facet Alexander, Drewitz
Alexis, Prévost
Pierre-François, Rodriguez
author_sort Alexander, Drewitz
title Critical exponents for a percolation model on transient graphs
title_short Critical exponents for a percolation model on transient graphs
title_full Critical exponents for a percolation model on transient graphs
title_fullStr Critical exponents for a percolation model on transient graphs
title_full_unstemmed Critical exponents for a percolation model on transient graphs
title_sort critical exponents for a percolation model on transient graphs
publishDate 2023
url https://link.springer.com/article/10.1007/s00222-022-01168-z
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7416
_version_ 1762184301745537024
score 8.8894005

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