Cluster tails for critical power-law inhomogeneous random graphs

DOI10.1007/s10955-018-1978-0zbMath1396.60007arXiv1404.1727OpenAlexW2106362077WikidataQ64907903 ScholiaQ64907903MaRDI QIDQ1753943

Johan S. H. van Leeuwaarden, Remco van der Hofstad, Sandra M. Kliem

Publication date: 29 May 2018

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.1727

zbMATH Keywords

large deviationsexponential tiltingcritical random graphsthinned Lévy processesinhomogeneous networkspower-law degrees

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Random graphs (graph-theoretic aspects) (05C80) Stochastic network models in operations research (90B15) Combinatorial probability (60C05)

Related Items

Large deviations for power-law thinned Lévy processes, Unusually large components in near-critical Erdős–Rényi graphs via ballot theorems, The probability of unusually large components for critical percolation on random \(d\)-regular graphs, Scale-free graphs with many edges, Big Jobs Arrive Early: From Critical Queues to Random Graphs, Heavy-tailed configuration models at criticality, The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs, Finite-pool queueing with heavy-tailed services, The probability of unusually large components in the near-critical Erdős–Rényi graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large deviations for power-law thinned Lévy processes
• Scaling limits for critical inhomogeneous random graphs with finite third moments
• Novel scaling limits for critical inhomogeneous random graphs
• Generating simple random graphs with prescribed degree distribution
• A local limit theorem for the critical random graph
• Correlation inequalities on some partially ordered sets
• Brownian excursions, critical random graphs and the multiplicative coalescent
• The entrance boundary of the multiplicative coalescent
• Exceptional times of the critical dynamical Erdős-Rényi graph
• On the largest component of the random graph at a nearcritical stage
• Connected components in random graphs with given expected degree sequences
• Critical behavior in inhomogeneous random graphs
• Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1.
• Asymptotic equivalence and contiguity of some random graphs
• Critical epidemics, random graphs, and Brownian motion with a parabolic drift
• The Volume of the Giant Component of a Random Graph with Given Expected Degrees
• The Evolution of Random Graphs
• Component behavior near the critical point of the random graph process
• Percolation
• The Structure of a Random Graph at the Point of the Phase Transition
• The Average Distance in a Random Graph with Given Expected Degrees
• The birth of the giant component
• The phase transition in inhomogeneous random graphs
• The average distances in random graphs with given expected degrees
• On a conditionally Poissonian graph process