A new encoding of coalescent processes: applications to the additive and multiplicative cases

DOI10.1007/s00440-015-0665-1zbMath1388.60035arXiv1409.4266OpenAlexW1747067133MaRDI QIDQ328790

Jean-François Marckert, Nicolas Broutin

Publication date: 21 October 2016

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4266

zbMATH Keywords

Cayley treerandom graphinvasion percolationPrim's algorithmadditive coalescentmultiplicative coalescent

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Continuous-time Markov processes on general state spaces (60J25) Combinatorics in computer science (68R05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05)

Related Items (9)

Parking on Cayley trees and frozen Erdős-Rényi ⋮ Models of random subtrees of a graph ⋮ Asymptotic behaviour of the first positions of uniform parking functions ⋮ Heavy-tailed configuration models at criticality ⋮ Scaling limit of dynamical percolation on critical Erdős-Rényi random graphs ⋮ A new combinatorial representation of the additive coalescent ⋮ Critical random forests ⋮ Stochastic block model in a new critical regime and the interacting multiplicative coalescent ⋮ The eternal multiplicative coalescent encoding via excursions of Lévy-type processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The augmented multiplicative coalescent, bounded size rules and critical dynamics of random graphs
• The continuum random tree. I
• Random trees and applications
• Stochastic coalescence with homogeneous-like interaction rates
• Erdős-Renyi random graphs \(+\) forest fires \(=\) self-organized criticality
• An invariance principle for random walk conditioned by a late return to zero
• Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
• Coalescent random forests
• The standard additive coalescent
• Brownian excursions, critical random graphs and the multiplicative coalescent
• Construction of Markovian coalescents
• A fragmentation process connected to Brownian motion
• Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
• One more approach to the convergence of the empirical process to the Brownian bridge
• The continuum limit of critical random graphs
• Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• Phase transition for Parking blocks, Brownian excursion and coalescence
• Capillary displacement and percolation in porous media
• Aggregation models with limited choice and the multiplicative coalescent
• On a conditionally Poissonian graph process
• Random Fragmentation and Coagulation Processes
• Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems

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