Percolation for the Finitary Random interlacements

Eviatar B. Procaccia; Jiayan Ye; Yuan Zhang

doi:10.30757/ALEA.V18-12

Percolation for the Finitary Random interlacements

Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang

Technion - Israel Institute of Technology, Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove a phase transition in the connectivity of finitary random interlacements FIu;T in Zd, with respect to the average stopping time T. For each u > 0, with probability one FIu;T has no infinite connected component for all sufficiently small T > 0, and a unique infinite connected component for all sufficiently large T < 1. This answers a question of Bowen (2019) in the special case of Zd.

Original language	English
Pages (from-to)	265-287
Number of pages	23
Journal	Alea
Volume	18
Issue number	1
DOIs	https://doi.org/10.30757/ALEA.V18-12
State	Published - 1 Jan 2020

All Science Journal Classification (ASJC) codes

Statistics and Probability

Access to Document

10.30757/ALEA.V18-12

Cite this

@article{91380c4b1592490399e883bd14244f30,

title = "Percolation for the Finitary Random interlacements",

abstract = "In this paper, we prove a phase transition in the connectivity of finitary random interlacements FIu;T in Zd, with respect to the average stopping time T. For each u > 0, with probability one FIu;T has no infinite connected component for all sufficiently small T > 0, and a unique infinite connected component for all sufficiently large T < 1. This answers a question of Bowen (2019) in the special case of Zd.",

author = "Procaccia, \{Eviatar B.\} and Jiayan Ye and Yuan Zhang",

note = "Funding Information: We would like to thank Dr. Bal?zs R?th for reminding us relevant studies that we had first overlooked. Part of this paper was written while the first two authors were visitors of Peking University. We would like to thank an anonymous referee for very detailed and helpful comments.",

year = "2020",

month = jan,

day = "1",

doi = "10.30757/ALEA.V18-12",

language = "الإنجليزيّة",

volume = "18",

pages = "265--287",

journal = "Alea",

issn = "1980-0436",

publisher = "Instituto Nacional de Matematica Pura e Aplicada",

number = "1",

}

TY - JOUR

T1 - Percolation for the Finitary Random interlacements

AU - Procaccia, Eviatar B.

AU - Ye, Jiayan

AU - Zhang, Yuan

N1 - Funding Information: We would like to thank Dr. Bal?zs R?th for reminding us relevant studies that we had first overlooked. Part of this paper was written while the first two authors were visitors of Peking University. We would like to thank an anonymous referee for very detailed and helpful comments.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In this paper, we prove a phase transition in the connectivity of finitary random interlacements FIu;T in Zd, with respect to the average stopping time T. For each u > 0, with probability one FIu;T has no infinite connected component for all sufficiently small T > 0, and a unique infinite connected component for all sufficiently large T < 1. This answers a question of Bowen (2019) in the special case of Zd.

AB - In this paper, we prove a phase transition in the connectivity of finitary random interlacements FIu;T in Zd, with respect to the average stopping time T. For each u > 0, with probability one FIu;T has no infinite connected component for all sufficiently small T > 0, and a unique infinite connected component for all sufficiently large T < 1. This answers a question of Bowen (2019) in the special case of Zd.

UR - http://www.scopus.com/inward/record.url?scp=85099134283&partnerID=8YFLogxK

U2 - 10.30757/ALEA.V18-12

DO - 10.30757/ALEA.V18-12

M3 - مقالة

SN - 1980-0436

VL - 18

SP - 265

EP - 287

JO - Alea

JF - Alea

IS - 1

ER -

Percolation for the Finitary Random interlacements

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this