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 - Article
AN - SCOPUS:85099134283
VL - 18
SP - 265
EP - 287
JO - Alea
JF - Alea
SN - 1980-0436
IS - 1
ER -