Limits of multiplicative inhomogeneous random graphs and Lévy trees: the continuum graphs

DOI10.1214/21-AAP1737zbMath1499.60017arXiv1804.05871OpenAlexW4293483769MaRDI QIDQ2083254

Minmin Wang, Nicolas Broutin, Thomas S. A. Duquesne

Publication date: 10 October 2022

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.05871

zbMATH Keywords

branching processrandom graphmultiplicative coalescentLévy tree

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• The component sizes of a critical random graph with given degree sequence
• Critical random graphs: limiting constructions and distributional properties
• Scaling limits for critical inhomogeneous random graphs with finite third moments
• The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs
• Continuum limit of critical inhomogeneous random graphs
• Novel scaling limits for critical inhomogeneous random graphs
• Generating simple random graphs with prescribed degree distribution
• Centered densities and fractal measures
• Universality for the distance in finite variance random graphs
• Branching processes in Lévy processes: The exploration process
• Brownian excursions, critical random graphs and the multiplicative coalescent
• The entrance boundary of the multiplicative coalescent
• Probabilistic and fractal aspects of Lévy trees
• Connected components in random graphs with given expected degree sequences
• Limits of multiplicative inhomogeneous random graphs and Lévy trees: limit theorems
• Universality for critical heavy-tailed network models: metric structure of maximal components
• Heavy-tailed configuration models at criticality
• The continuum random tree. III
• The continuum limit of critical random graphs
• Probability and real trees. Ecole d'Eté de Probabilités de Saint-Flour XXXV -- 2005. Lecture given at the Saint-Flour probability summer school, July 6--23, 2005.
• Random Graphs and Complex Networks
• Critical behavior in inhomogeneous random graphs
• Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1.
• Introduction to Random Graphs
• Asymptotic equivalence and contiguity of some random graphs
• Packing Measure, and its Evaluation for a Brownian Path
• Dynamical Processes on Complex Networks
• The phase transition in inhomogeneous random graphs
• On a conditionally Poissonian graph process
• Functions continuous and singular with respect to a Hausdorff measure