Matches in SemOpenAlex for { <https://semopenalex.org/work/W4226348083> ?p ?o ?g. }
Showing items 1 to 53 of
53
with 100 items per page.
- W4226348083 abstract "Consider $n$ identical Kuramoto oscillators on a random graph. Specifically, consider ER random graphs in which any two oscillators are bidirectionally coupled with unit strength, independently and at random, with probability $0leq pleq 1$. We say that a network is globally synchronizing if the oscillators converge to the all-in-phase synchronous state for almost all initial conditions. Is there a critical threshold for $p$ above which global synchrony is extremely likely but below which it is extremely rare? It is suspected that a critical threshold exists and is close to the so-called connectivity threshold, namely, $psim log(n)/n$ for $n gg 1$. Ling, Xu, and Bandeira made the first progress toward proving a result in this direction: they showed that if $pgg log(n)/n^{1/3}$, then ER networks of Kuramoto oscillators are globally synchronizing with high probability as $nrightarrowinfty$. Here we improve that result by showing that $pgg log^2(n)/n$ suffices. Our estimates are explicit: for example, we can say that there is more than a $99.9996%$ chance that a random network with $n = 10^6$ and $p>0.01117$ is globally synchronizing." @default.
- W4226348083 created "2022-05-05" @default.
- W4226348083 creator A5003110773 @default.
- W4226348083 creator A5027770198 @default.
- W4226348083 creator A5029418921 @default.
- W4226348083 date "2022-03-07" @default.
- W4226348083 modified "2023-09-24" @default.
- W4226348083 title "A global synchronization theorem for oscillators on a random graph" @default.
- W4226348083 doi "https://doi.org/10.48550/arxiv.2203.03152" @default.
- W4226348083 hasPublicationYear "2022" @default.
- W4226348083 type Work @default.
- W4226348083 citedByCount "0" @default.
- W4226348083 crossrefType "posted-content" @default.
- W4226348083 hasAuthorship W4226348083A5003110773 @default.
- W4226348083 hasAuthorship W4226348083A5027770198 @default.
- W4226348083 hasAuthorship W4226348083A5029418921 @default.
- W4226348083 hasBestOaLocation W42263480831 @default.
- W4226348083 hasConcept C111097370 @default.
- W4226348083 hasConcept C114614502 @default.
- W4226348083 hasConcept C118615104 @default.
- W4226348083 hasConcept C132525143 @default.
- W4226348083 hasConcept C162932704 @default.
- W4226348083 hasConcept C184720557 @default.
- W4226348083 hasConcept C2778562939 @default.
- W4226348083 hasConcept C2780042749 @default.
- W4226348083 hasConcept C33923547 @default.
- W4226348083 hasConcept C47458327 @default.
- W4226348083 hasConceptScore W4226348083C111097370 @default.
- W4226348083 hasConceptScore W4226348083C114614502 @default.
- W4226348083 hasConceptScore W4226348083C118615104 @default.
- W4226348083 hasConceptScore W4226348083C132525143 @default.
- W4226348083 hasConceptScore W4226348083C162932704 @default.
- W4226348083 hasConceptScore W4226348083C184720557 @default.
- W4226348083 hasConceptScore W4226348083C2778562939 @default.
- W4226348083 hasConceptScore W4226348083C2780042749 @default.
- W4226348083 hasConceptScore W4226348083C33923547 @default.
- W4226348083 hasConceptScore W4226348083C47458327 @default.
- W4226348083 hasLocation W42263480831 @default.
- W4226348083 hasOpenAccess W4226348083 @default.
- W4226348083 hasPrimaryLocation W42263480831 @default.
- W4226348083 hasRelatedWork W1488962991 @default.
- W4226348083 hasRelatedWork W1602031491 @default.
- W4226348083 hasRelatedWork W2000125983 @default.
- W4226348083 hasRelatedWork W2065303481 @default.
- W4226348083 hasRelatedWork W2167905212 @default.
- W4226348083 hasRelatedWork W2297311436 @default.
- W4226348083 hasRelatedWork W2783165419 @default.
- W4226348083 hasRelatedWork W2963032256 @default.
- W4226348083 hasRelatedWork W4226348083 @default.
- W4226348083 hasRelatedWork W4292952218 @default.
- W4226348083 isParatext "false" @default.
- W4226348083 isRetracted "false" @default.
- W4226348083 workType "article" @default.