The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees

DOI10.1214/22-AOP1587zbMath1504.05262arXiv2002.04954MaRDI QIDQ2105139

Guillaume Conchon-Kerjan, Christina Goldschmidt

Publication date: 8 December 2022

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

Full work available at URL: https://arxiv.org/abs/2002.04954

zbMATH Keywords

scaling limitrandom graphstable Lévy processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05) Stable stochastic processes (60G52)

Related Items (5)

Universality for critical heavy-tailed network models: metric structure of maximal components ⋮ The scaling limit of a critical random directed graph ⋮ Stable graphs: distributions and line-breaking construction ⋮ Parking on Cayley trees and frozen Erdős-Rényi ⋮ Network models: structure and function. Abstracts from the workshop held December 10--16, 2017

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The component sizes of a critical random graph with given degree sequence
• The augmented multiplicative coalescent, bounded size rules and critical dynamics of random graphs
• Critical window for the configuration model: finite third moment degrees
• 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
• The continuum random tree. I
• Size-biased permutation of a finite sequence with independent and identically distributed terms
• Random trees and applications
• Brownian excursion area, wright's constants in graph enumeration, and other Brownian areas
• On percolation in random graphs with given vertex degrees
• A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
• Factorizing Laplace exponents in a spectrally positive Lévy process
• The asymptotic number of labeled graphs with given degree sequences
• Brownian excursions, critical random graphs and the multiplicative coalescent
• The entrance boundary of the multiplicative coalescent
• A limit theorem for the contour process of conditioned Galton-Watson trees
• Logarithmic combinatorial structures: A probabilistic approach
• Self-similar fragmentation derived from the stable tree. I: Splitting at heights
• The depth first processes of Galton-Watson trees converge to the same Brownian excursion
• The scaling limit of the minimum spanning tree of the complete graph
• Self-similar fragmentations derived from the stable tree. II: Splitting at nodes
• Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
• Progress in high-dimensional percolation and random graphs
• 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
• Sub-exponential tail bounds for conditioned stable Bienaymé-Galton-Watson trees
• The continuum random tree. III
• Rigid representations of the multiplicative coalescent with linear deletion
• The continuum limit of critical random graphs
• Critical percolation on scale-free random graphs: new universality class for the configuration model
• Avoiding a giant component
• Brownian Motion, Martingales, and Stochastic Calculus
• Random Graphs and Complex Networks
• Critical behavior in inhomogeneous random graphs
• Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1.
• The Phase Transition in the Configuration Model
• Critical percolation on random regular graphs
• A new approach to the giant component problem
• The Size of the Giant Component of a Random Graph with a Given Degree Sequence
• A critical point for random graphs with a given degree sequence
• Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees
• On a conditionally Poissonian graph process
• Bounded-Size Rules: The Barely Subcritical Regime
• An Introduction to the Theory of Point Processes
• Probability

This page was built for publication: The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees