FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3048192146> ?p ?o ?g. }

• W3048192146 endingPage "447" @default.
• W3048192146 startingPage "364" @default.
• W3048192146 abstract "We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed positive edge weights. We consider the case where the lower extreme values of the edge weights are highly separated. This model exhibits strong disorder and a crossover between local and global scales. Local neighborhoods are related to invasion percolation that display self-organised criticality. Globally, the edges with relevant edge weights form a barely supercritical Erdős-Rényi random graph that can be described by branching processes. This near-critical behaviour gives rise to optimal paths that are considerably longer than logarithmic in the number of vertices, interpolating between random graph and minimal spanning tree path lengths. Crucial to our approach is the quantification of the extreme-value behavior of small edge weights in terms of a sequence of parameters (sn)n≥1 that characterises the different universality classes for first passage percolation on the complete graph. We investigate the case where sn→∞ with sn=o(n1/3) , which corresponds to the barely supercritical setting. We identify the scaling limit of the weight of the optimal path between two vertices, and we prove that the number of edges in this path obeys a central limit theorem with mean approximately snlog(n/sn3) and variance sn2log(n/sn3) . Remarkably, our proof also applies to n-dependent edge weights of the form Esn , where E is an exponential random variable with mean 1, thus settling a conjecture of Bhamidi et al. (Weak disorder asymptotics in the stochastic meanfield model of distance. Ann Appl Probab 22(1):29-69, 2012). The proof relies on a decomposition of the smallest-weight tree into an initial part following invasion percolation dynamics, and a main part following branching process dynamics. The initial part has been studied in Eckhoff et al. (Long paths in first passage percolation on the complete graph I. Local PWIT dynamics. Electron. J. Probab. 25:1-45, 2020. 10.1214/20-EJP484); the current paper focuses on the global branching dynamics." @default.
• W3048192146 created "2020-08-13" @default.
• W3048192146 creator A5003581347 @default.
• W3048192146 creator A5034587660 @default.
• W3048192146 creator A5047780394 @default.
• W3048192146 creator A5085664045 @default.
• W3048192146 date "2020-08-06" @default.
• W3048192146 modified "2023-09-23" @default.
• W3048192146 title "Long Paths in First Passage Percolation on the Complete Graph II. Global Branching Dynamics" @default.
• W3048192146 cites W1677378690 @default.
• W3048192146 cites W1908254782 @default.
• W3048192146 cites W1996534617 @default.
• W3048192146 cites W2008620264 @default.
• W3048192146 cites W2028922813 @default.
• W3048192146 cites W2031541804 @default.
• W3048192146 cites W2038033449 @default.
• W3048192146 cites W2073886569 @default.
• W3048192146 cites W2100172709 @default.
• W3048192146 cites W2112911366 @default.
• W3048192146 cites W2121526364 @default.
• W3048192146 cites W2143834312 @default.
• W3048192146 cites W2148606196 @default.
• W3048192146 cites W2159644837 @default.
• W3048192146 cites W2290127356 @default.
• W3048192146 cites W2502254989 @default.
• W3048192146 cites W2604389799 @default.
• W3048192146 cites W2794047718 @default.
• W3048192146 cites W2962725771 @default.
• W3048192146 cites W2962953861 @default.
• W3048192146 cites W2963835249 @default.
• W3048192146 cites W2964161254 @default.
• W3048192146 cites W3042614504 @default.
• W3048192146 cites W3048192146 @default.
• W3048192146 cites W3100885978 @default.
• W3048192146 cites W3103158139 @default.
• W3048192146 cites W3103295595 @default.
• W3048192146 cites W3104374707 @default.
• W3048192146 cites W3104622381 @default.
• W3048192146 cites W3105104202 @default.
• W3048192146 cites W4230556510 @default.
• W3048192146 cites W4238452917 @default.
• W3048192146 doi "https://doi.org/10.1007/s10955-020-02585-1" @default.
• W3048192146 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/7462937" @default.
• W3048192146 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/32921809" @default.
• W3048192146 hasPublicationYear "2020" @default.
• W3048192146 type Work @default.
• W3048192146 sameAs 3048192146 @default.
• W3048192146 citedByCount "2" @default.
• W3048192146 countsByYear W30481921462020 @default.
• W3048192146 countsByYear W30481921462023 @default.
• W3048192146 crossrefType "journal-article" @default.
• W3048192146 hasAuthorship W3048192146A5003581347 @default.
• W3048192146 hasAuthorship W3048192146A5034587660 @default.
• W3048192146 hasAuthorship W3048192146A5047780394 @default.
• W3048192146 hasAuthorship W3048192146A5085664045 @default.
• W3048192146 hasBestOaLocation W30481921461 @default.
• W3048192146 hasConcept C105795698 @default.
• W3048192146 hasConcept C114614502 @default.
• W3048192146 hasConcept C118615104 @default.
• W3048192146 hasConcept C121332964 @default.
• W3048192146 hasConcept C122123141 @default.
• W3048192146 hasConcept C132525143 @default.
• W3048192146 hasConcept C134306372 @default.
• W3048192146 hasConcept C141513077 @default.
• W3048192146 hasConcept C177255742 @default.
• W3048192146 hasConcept C22590252 @default.
• W3048192146 hasConcept C2729557 @default.
• W3048192146 hasConcept C2780990831 @default.
• W3048192146 hasConcept C33923547 @default.
• W3048192146 hasConcept C39927690 @default.
• W3048192146 hasConcept C47458327 @default.
• W3048192146 hasConcept C54385418 @default.
• W3048192146 hasConcept C62520636 @default.
• W3048192146 hasConcept C69990965 @default.
• W3048192146 hasConceptScore W3048192146C105795698 @default.
• W3048192146 hasConceptScore W3048192146C114614502 @default.
• W3048192146 hasConceptScore W3048192146C118615104 @default.
• W3048192146 hasConceptScore W3048192146C121332964 @default.
• W3048192146 hasConceptScore W3048192146C122123141 @default.
• W3048192146 hasConceptScore W3048192146C132525143 @default.
• W3048192146 hasConceptScore W3048192146C134306372 @default.
• W3048192146 hasConceptScore W3048192146C141513077 @default.
• W3048192146 hasConceptScore W3048192146C177255742 @default.
• W3048192146 hasConceptScore W3048192146C22590252 @default.
• W3048192146 hasConceptScore W3048192146C2729557 @default.
• W3048192146 hasConceptScore W3048192146C2780990831 @default.
• W3048192146 hasConceptScore W3048192146C33923547 @default.
• W3048192146 hasConceptScore W3048192146C39927690 @default.
• W3048192146 hasConceptScore W3048192146C47458327 @default.
• W3048192146 hasConceptScore W3048192146C54385418 @default.
• W3048192146 hasConceptScore W3048192146C62520636 @default.
• W3048192146 hasConceptScore W3048192146C69990965 @default.
• W3048192146 hasFunder F4320321800 @default.
• W3048192146 hasIssue "2" @default.
• W3048192146 hasLocation W30481921461 @default.
• W3048192146 hasLocation W30481921462 @default.
• W3048192146 hasLocation W30481921463 @default.
• W3048192146 hasLocation W30481921464 @default.

• next