Matches in SemOpenAlex for { <https://semopenalex.org/work/W2888549097> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2888549097 abstract "Around 2008, Schramm conjectured that the critical probabilities for Bernoulli bond percolation satisfy the following continuity property: If $(G_n)_{ngeq 1}$ is a sequence of transitive graphs converging locally to a transitive graph $G$ and $limsup_{ntoinfty} p_c(G_n) < 1$, then $ p_c(G_n)to p_c(G)$ as $ntoinfty$. We verify this conjecture under the additional hypothesis that there is a uniform exponential lower bound on the volume growth of the graphs in question. The result is new even in the case that the sequence of graphs is uniformly nonamenable. In the unimodular case, this result is obtained as a corollary to the following theorem of independent interest: For every $g>1$ and $M<infty$, there exist positive constants $C=C(g,M)$ and $delta=delta(g,M)$ such that if $G$ is a transitive unimodular graph with degree at most $M$ and growth $operatorname{gr}(G) := inf_{rgeq 1} |B(o,r)|^{1/r}geq g$, then [ mathbf{P}_{p_c} bigl(|K_o|geq nbigr) leq C n^{-delta} ] for every $ngeq 1$, where $K_o$ is the cluster of the root vertex $o$. The proof of this inequality makes use of new universal bounds on the probabilities of certain two-arm events, which hold for every unimodular transitive graph." @default.
- W2888549097 created "2018-08-31" @default.
- W2888549097 creator A5060156386 @default.
- W2888549097 date "2018-08-27" @default.
- W2888549097 modified "2023-09-27" @default.
- W2888549097 title "Locality of the critical probability for transitive graphs of exponential growth" @default.
- W2888549097 cites W121824094 @default.
- W2888549097 cites W1487891262 @default.
- W2888549097 cites W155255179 @default.
- W2888549097 cites W1980051489 @default.
- W2888549097 cites W2008685166 @default.
- W2888549097 cites W2011203762 @default.
- W2888549097 cites W2032983973 @default.
- W2888549097 cites W2035705692 @default.
- W2888549097 cites W2037071998 @default.
- W2888549097 cites W2040264077 @default.
- W2888549097 cites W2047377731 @default.
- W2888549097 cites W2049086589 @default.
- W2888549097 cites W2069036239 @default.
- W2888549097 cites W2075473854 @default.
- W2888549097 cites W2093600087 @default.
- W2888549097 cites W2108022501 @default.
- W2888549097 cites W2137303843 @default.
- W2888549097 cites W2165114349 @default.
- W2888549097 cites W2398326034 @default.
- W2888549097 cites W2512750173 @default.
- W2888549097 cites W2607779876 @default.
- W2888549097 cites W2753603789 @default.
- W2888549097 cites W2767306879 @default.
- W2888549097 cites W2769174420 @default.
- W2888549097 cites W2962980368 @default.
- W2888549097 cites W2963188338 @default.
- W2888549097 cites W2963735720 @default.
- W2888549097 cites W2982239601 @default.
- W2888549097 cites W3101626631 @default.
- W2888549097 hasPublicationYear "2018" @default.
- W2888549097 type Work @default.
- W2888549097 sameAs 2888549097 @default.
- W2888549097 citedByCount "1" @default.
- W2888549097 countsByYear W28885490972018 @default.
- W2888549097 crossrefType "posted-content" @default.
- W2888549097 hasAuthorship W2888549097A5060156386 @default.
- W2888549097 hasConcept C114614502 @default.
- W2888549097 hasConcept C118615104 @default.
- W2888549097 hasConcept C191399111 @default.
- W2888549097 hasConcept C201958917 @default.
- W2888549097 hasConcept C2780990831 @default.
- W2888549097 hasConcept C33923547 @default.
- W2888549097 hasConceptScore W2888549097C114614502 @default.
- W2888549097 hasConceptScore W2888549097C118615104 @default.
- W2888549097 hasConceptScore W2888549097C191399111 @default.
- W2888549097 hasConceptScore W2888549097C201958917 @default.
- W2888549097 hasConceptScore W2888549097C2780990831 @default.
- W2888549097 hasConceptScore W2888549097C33923547 @default.
- W2888549097 hasLocation W28885490971 @default.
- W2888549097 hasOpenAccess W2888549097 @default.
- W2888549097 hasPrimaryLocation W28885490971 @default.
- W2888549097 hasRelatedWork W1853219099 @default.
- W2888549097 hasRelatedWork W1971626346 @default.
- W2888549097 hasRelatedWork W2072775530 @default.
- W2888549097 hasRelatedWork W2073982255 @default.
- W2888549097 hasRelatedWork W2398326034 @default.
- W2888549097 hasRelatedWork W2803355438 @default.
- W2888549097 hasRelatedWork W2948759546 @default.
- W2888549097 hasRelatedWork W2952331453 @default.
- W2888549097 hasRelatedWork W2963340133 @default.
- W2888549097 hasRelatedWork W2963969197 @default.
- W2888549097 hasRelatedWork W2964151775 @default.
- W2888549097 hasRelatedWork W2969799327 @default.
- W2888549097 hasRelatedWork W2977221212 @default.
- W2888549097 hasRelatedWork W3010444613 @default.
- W2888549097 hasRelatedWork W3036631610 @default.
- W2888549097 hasRelatedWork W3127690597 @default.
- W2888549097 hasRelatedWork W3127987152 @default.
- W2888549097 hasRelatedWork W3131168989 @default.
- W2888549097 hasRelatedWork W3153466127 @default.
- W2888549097 hasRelatedWork W3196558748 @default.
- W2888549097 isParatext "false" @default.
- W2888549097 isRetracted "false" @default.
- W2888549097 magId "2888549097" @default.
- W2888549097 workType "article" @default.