Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions

Fuente: arXiv
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Main Authors: Bi, Yijie, Cai, Zhenhao, Li, Xinyi, Ráth, Balázs, Zhang, Yuan
Format: Preprint
Published: 2025
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_version_ 1866914096594550784
author Bi, Yijie
Cai, Zhenhao
Li, Xinyi
Ráth, Balázs
Zhang, Yuan
author_facet Bi, Yijie
Cai, Zhenhao
Li, Xinyi
Ráth, Balázs
Zhang, Yuan
contents We establish sharp asymptotic bounds for the critical intensity of the Finitary Random Interlacements (FRI) model in four and higher dimensions with general trajectory length distributions. Our proof reveals that the construction of near-critical FRI clusters in four and higher dimensions is essentially analogous to a Galton-Watson process, whose expected number of offspring corresponds to the capacity of a random walk killed at the given length.
format Preprint
id arxiv_https___arxiv_org_abs_2510_14734
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions
Bi, Yijie
Cai, Zhenhao
Li, Xinyi
Ráth, Balázs
Zhang, Yuan
Probability
60K35, 82B43, 60G50, 82B41
We establish sharp asymptotic bounds for the critical intensity of the Finitary Random Interlacements (FRI) model in four and higher dimensions with general trajectory length distributions. Our proof reveals that the construction of near-critical FRI clusters in four and higher dimensions is essentially analogous to a Galton-Watson process, whose expected number of offspring corresponds to the capacity of a random walk killed at the given length.
title Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions
topic Probability
60K35, 82B43, 60G50, 82B41
url https://arxiv.org/abs/2510.14734