Convergence of Achlioptas Processes via Differential Equations with Unique Solutions

DOI10.1017/S0963548315000218zbMath1371.05273arXiv1111.6179MaRDI QIDQ5364268

Oliver Riordan, Lutz Warnke

Publication date: 4 October 2017

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.6179

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05) Ordinary differential equations and systems with randomness (34F05)

Related Items

Network models: structure and function. Abstracts from the workshop held December 10--16, 2017, Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: a study within combinatorial framework, On the normality of giant components

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Achlioptas process phase transitions are continuous
• Phase transitions for modified Erdős--Rényi processes
• Handbook of large-scale random networks
• Birth control for giants
• A central limit theorem via differential equations
• Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
• Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent
• Differential equations for random processes and random graphs
• Avoiding a giant component
• The Bohman-Frieze process near criticality
• Networking—Smoothly Does It
• The evolution of subcritical Achlioptas processes
• Balanced Allocations
• Probability: A Graduate Course
• Aggregation models with limited choice and the multiplicative coalescent
• Creating a Giant Component
• The phase transition in inhomogeneous random graphs
• Bounded-Size Rules: The Barely Subcritical Regime
• Explosive Percolation in Random Networks