TY - JOUR
T1 - Approximation on slabs and uniqueness for Bernoulli percolation with a sublattice of defects
AU - de Lima, Bernardo N.B.
AU - Martineau, Sébastien
AU - Sanna, Humberto C.
AU - Valesin, Daniel
N1 - Funding Information:
Received by the editors September 20th, 2021; accepted August 18th, 2022. 2010 Mathematics Subject Classification. 60K35, 82B43. Key words and phrases. Inhomogeneous percolation; Uniqueness; Critical curve; Grimmett–Marstrand Theorem. The research of B.N.B.L. was supported in part by CNPq grant 305811/2018-5, FAPEMIG (Programa Pesquisador Mineiro) and FAPERJ (Pronex E-26/010.001269/2016). The research of H.C.S was supported in part by CAPES – Finance Code 001, and by CNPq grant 140548/2013-0. H.C.S. would like to thank CAPES for the financial support from the PrInt scholarship and the University of Groningen for the hospitality during his internship at Bernoulli Institute.
Publisher Copyright:
© 2022,Alea (Rio de Janeiro).All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - Let Ld = (Zd;Ed) be the d-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on Ld in which every edge inside the s-dimensional sublattice (Formula Presented) is open with probability q and every other edge is open with probability p.
AB - Let Ld = (Zd;Ed) be the d-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on Ld in which every edge inside the s-dimensional sublattice (Formula Presented) is open with probability q and every other edge is open with probability p.
KW - Critical curve
KW - Grimmett–Marstrand Theorem
KW - Inhomogeneous percolation
KW - Uniqueness
UR - http://www.scopus.com/inward/record.url?scp=85147801011&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85147801011
SN - 1980-0436
VL - 19
SP - 1767
EP - 1797
JO - Alea (Rio de Janeiro)
JF - Alea (Rio de Janeiro)
IS - 2
ER -