Matches in SemOpenAlex for { <https://semopenalex.org/work/W2017452431> ?p ?o ?g. }
- W2017452431 endingPage "51" @default.
- W2017452431 startingPage "17" @default.
- W2017452431 abstract "In majority bootstrap percolation on a graph G , an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain infected forever. We say that percolation occurs if eventually every vertex is infected. The elements of the set of initially infected vertices, A ⊂ V ( G ), are normally chosen independently at random, each with probability p , say. This process has been extensively studied on the sequence of torus graphs [ n ] d , for n = 1,2, . . ., where d = d ( n ) is either fixed or a very slowly growing function of n . For example, Cerf and Manzo [17] showed that the critical probability is o (1) if d ( n ) ≤ log * n , i.e. , if p = p ( n ) is bounded away from zero then the probability of percolation on [ n ] d tends to one as n → ∞. In this paper we study the case when the growth of d to ∞ is not excessively slow; in particular, we show that the critical probability is 1/2 + o (1) if d ≥ (log log n ) 2 log log log n , and give much stronger bounds in the case that G is the hypercube, [2] d ." @default.
- W2017452431 created "2016-06-24" @default.
- W2017452431 creator A5015732625 @default.
- W2017452431 creator A5029881267 @default.
- W2017452431 creator A5059910732 @default.
- W2017452431 date "2009-03-01" @default.
- W2017452431 modified "2023-10-03" @default.
- W2017452431 title "Majority Bootstrap Percolation on the Hypercube" @default.
- W2017452431 cites W1898632731 @default.
- W2017452431 cites W1972354222 @default.
- W2017452431 cites W1989844253 @default.
- W2017452431 cites W1995341919 @default.
- W2017452431 cites W2008176768 @default.
- W2017452431 cites W2026620883 @default.
- W2017452431 cites W2027223596 @default.
- W2017452431 cites W2027508917 @default.
- W2017452431 cites W2035529977 @default.
- W2017452431 cites W2045453971 @default.
- W2017452431 cites W2055616644 @default.
- W2017452431 cites W2067253751 @default.
- W2017452431 cites W2075997628 @default.
- W2017452431 cites W2090921949 @default.
- W2017452431 cites W2093333397 @default.
- W2017452431 cites W2107074561 @default.
- W2017452431 cites W2108551278 @default.
- W2017452431 cites W2125271247 @default.
- W2017452431 cites W2158967324 @default.
- W2017452431 cites W2171265914 @default.
- W2017452431 cites W3098697633 @default.
- W2017452431 cites W390146837 @default.
- W2017452431 doi "https://doi.org/10.1017/s0963548308009322" @default.
- W2017452431 hasPublicationYear "2009" @default.
- W2017452431 type Work @default.
- W2017452431 sameAs 2017452431 @default.
- W2017452431 citedByCount "55" @default.
- W2017452431 countsByYear W20174524312012 @default.
- W2017452431 countsByYear W20174524312013 @default.
- W2017452431 countsByYear W20174524312014 @default.
- W2017452431 countsByYear W20174524312015 @default.
- W2017452431 countsByYear W20174524312016 @default.
- W2017452431 countsByYear W20174524312017 @default.
- W2017452431 countsByYear W20174524312018 @default.
- W2017452431 countsByYear W20174524312020 @default.
- W2017452431 countsByYear W20174524312021 @default.
- W2017452431 countsByYear W20174524312022 @default.
- W2017452431 countsByYear W20174524312023 @default.
- W2017452431 crossrefType "journal-article" @default.
- W2017452431 hasAuthorship W2017452431A5015732625 @default.
- W2017452431 hasAuthorship W2017452431A5029881267 @default.
- W2017452431 hasAuthorship W2017452431A5059910732 @default.
- W2017452431 hasBestOaLocation W20174524312 @default.
- W2017452431 hasConcept C114614502 @default.
- W2017452431 hasConcept C118615104 @default.
- W2017452431 hasConcept C132525143 @default.
- W2017452431 hasConcept C134306372 @default.
- W2017452431 hasConcept C169760540 @default.
- W2017452431 hasConcept C2524010 @default.
- W2017452431 hasConcept C2780457167 @default.
- W2017452431 hasConcept C33923547 @default.
- W2017452431 hasConcept C34388435 @default.
- W2017452431 hasConcept C50820777 @default.
- W2017452431 hasConcept C63553672 @default.
- W2017452431 hasConcept C80899671 @default.
- W2017452431 hasConcept C86803240 @default.
- W2017452431 hasConcept C9767117 @default.
- W2017452431 hasConceptScore W2017452431C114614502 @default.
- W2017452431 hasConceptScore W2017452431C118615104 @default.
- W2017452431 hasConceptScore W2017452431C132525143 @default.
- W2017452431 hasConceptScore W2017452431C134306372 @default.
- W2017452431 hasConceptScore W2017452431C169760540 @default.
- W2017452431 hasConceptScore W2017452431C2524010 @default.
- W2017452431 hasConceptScore W2017452431C2780457167 @default.
- W2017452431 hasConceptScore W2017452431C33923547 @default.
- W2017452431 hasConceptScore W2017452431C34388435 @default.
- W2017452431 hasConceptScore W2017452431C50820777 @default.
- W2017452431 hasConceptScore W2017452431C63553672 @default.
- W2017452431 hasConceptScore W2017452431C80899671 @default.
- W2017452431 hasConceptScore W2017452431C86803240 @default.
- W2017452431 hasConceptScore W2017452431C9767117 @default.
- W2017452431 hasIssue "1-2" @default.
- W2017452431 hasLocation W20174524311 @default.
- W2017452431 hasLocation W20174524312 @default.
- W2017452431 hasLocation W20174524313 @default.
- W2017452431 hasOpenAccess W2017452431 @default.
- W2017452431 hasPrimaryLocation W20174524311 @default.
- W2017452431 hasRelatedWork W1738343536 @default.
- W2017452431 hasRelatedWork W1984834024 @default.
- W2017452431 hasRelatedWork W2004949669 @default.
- W2017452431 hasRelatedWork W2026407613 @default.
- W2017452431 hasRelatedWork W2042483675 @default.
- W2017452431 hasRelatedWork W2357174291 @default.
- W2017452431 hasRelatedWork W2766968228 @default.
- W2017452431 hasRelatedWork W2953495953 @default.
- W2017452431 hasRelatedWork W2964130894 @default.
- W2017452431 hasRelatedWork W636636047 @default.
- W2017452431 hasVolume "18" @default.
- W2017452431 isParatext "false" @default.
- W2017452431 isRetracted "false" @default.