Scaling Limits of Random Trees and Random Graphs

DOI10.1007/978-3-030-32011-9_1zbMath1442.05209OpenAlexW2993980234MaRDI QIDQ3294677

Christina Goldschmidt

Publication date: 29 June 2020

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-32011-9_1

zbMATH Keywords

random graphsrandom treesscaling limitsBrownian continuum random tree\( \mathbb{R} \)-trees

Mathematics Subject Classification ID

Trees (05C05) Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05)

Related Items

Growing random graphs with a preferential attachment structure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
• 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
• Continuum limit of critical inhomogeneous random graphs
• Novel scaling limits for critical inhomogeneous random graphs
• The continuum random tree. I
• Random trees and applications
• An invariance principle for random walk conditioned by a late return to zero
• The uniform random tree in a Brownian excursion
• Brownian excursions, critical random graphs and the multiplicative coalescent
• 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
• The genealogy of self-similar fragmentations with negative index as a continuum random tree
• Universality for critical heavy-tailed network models: metric structure of maximal components
• The continuum random tree. III
• The continuum limit of critical random graphs
• Random real trees
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• A line-breaking construction of the stable trees
• The Phase Transition in the Configuration Model
• 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
• Scaling limits of random trees and planar maps