The 2D-directed spanning forest converges to the Brownian web

DOI10.1214/20-AOP1478zbMath1476.60021arXiv1805.09399OpenAlexW2803760053MaRDI QIDQ2227719

Anish Sarkar, Viet Chi Tran, David Coupier, Kumarjit Saha

Publication date: 15 February 2021

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

Full work available at URL: https://arxiv.org/abs/1805.09399

zbMATH Keywords

Poisson point processesBrownian webdirected spanning forestrenewal timesgeometrical interactionsrandom geometric tree

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Functional limit theorems; invariance principles (60F17)

Related Items (5)

Directed, cylindric and radial Brownian webs ⋮ A drainage network with dependence and the Brownian web ⋮ The bi-dimensional directed IDLA forest ⋮ The directed spanning forest in the hyperbolic space ⋮ Two directed non-planar random networks and their scaling limits

Cites Work

• Hack's law in a drainage network model: a Brownian web approach
• Random directed forest and the Brownian web
• Brownian web in the scaling limit of supercritical oriented percolation in dimension \(1 + 1\)
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• Sublinearity of the number of semi-infinite branches for geometric random trees
• Convergence of coalescing nonsimple random walks to the Brownian web
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• The Brownian net
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• Two-dimensional Poisson trees converge to the Brownian web
• Directed, cylindric and radial Brownian webs
• Scaling Limit for a Drainage Network Model
• Applied Probability and Queues
• The 2D‐directed spanning forest is almost surely a tree
• Semi-Infinite Paths of the Two-Dimensional Radial Spanning Tree
• Coalescing Brownian flows: a new approach
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