Premium
Absence of site percolation at criticality in ℤ 2 × { 0 , 1 }
Author(s) -
Damron Michael,
Newman Charles M.,
Sidoravicius Vladas
Publication year - 2015
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20544
Subject(s) - percolation (cognitive psychology) , criticality , mathematics , directed percolation , extension (predicate logic) , boundary (topology) , graph , struct , statistical physics , combinatorics , discrete mathematics , critical exponent , phase transition , physics , condensed matter physics , computer science , mathematical analysis , neuroscience , nuclear physics , biology , programming language
In this note we consider site percolation on a two dimensional sandwich of thickness two, the graphℤ 2 × { 0 , 1 } . We prove that there is no percolation at the critical point. The same arguments are valid for a sandwich of thickness three with periodic boundary conditions. It remains an open problem to extend this result to other sandwiches. “Note added in proof: This extension has recently been accomplished in arXiv 1401.7130.” © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 328–340, 2015
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom