On scaling limits of random trees and maps with a prescribed degree sequence

DOI10.5802/ahl.125zbMath1487.05074arXiv1903.06138OpenAlexW3204062795WikidataQ113196024 ScholiaQ113196024MaRDI QIDQ2136415

Cyril Marzouk

Publication date: 10 May 2022

Published in: Annales Henri Lebesgue (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.06138

zbMATH Keywords

random treesscaling limitsrandom maps

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Geometric probability and stochastic geometry (60D05) Random graphs (graph-theoretic aspects) (05C80) Planar graphs; geometric and topological aspects of graph theory (05C10) Functional limit theorems; invariance principles (60F17) Graph designs and isomorphic decomposition (05C51)

Related Items

The mesoscopic geometry of sparse random maps ⋮ Large deviation local limit theorems and limits of biconditioned planar maps ⋮ Universal height and width bounds for random trees ⋮ The volume measure of the Brownian sphere is a Hausdorff measure

Cites Work

• Unnamed Item
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• Rescaled bipartite planar maps converge to the Brownian map
• Uniqueness and universality of the Brownian map
• The Brownian map is the scaling limit of uniform random plane quadrangulations
• Invariance principles for Galton-Watson trees conditioned on the number of leaves
• Compact Brownian surfaces. I: Brownian disks
• Scaling limits of random planar maps with large faces
• Scaling limits for random quadrangulations of positive genus
• The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection
• Vertices with fixed outdegrees in large Galton-Watson trees
• Random trees and applications
• Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere
• On the sphericity of scaling limits of random planar quadrangulations
• The depth first processes of Galton-Watson trees converge to the same Brownian excursion
• The scaling limit of random simple triangulations and random simple quadrangulations
• Path transformations of first passage bridges
• Planar maps as labeled mobiles
• The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity
• The Brownian cactus. I: Scaling limits of discrete cactuses
• Convergence of non-bipartite maps via symmetrization of labeled trees
• The boundary of random planar maps via looptrees
• Notes on random walks in the Cauchy domain of attraction
• Exact tail asymptotics of the supremum attained by a Lévy process
• Limit theorems for conditioned non-generic Galton-Watson trees
• Scaling limits of random planar maps with a unique large face
• Sub-exponential tail bounds for conditioned stable Bienaymé-Galton-Watson trees
• The continuum random tree. III
• The topological structure of scaling limits of large planar maps
• Condensation in critical Cauchy Bienaymé-Galton-Watson trees
• Invariance principles for random bipartite planar maps
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• Tail bounds for the height and width of a random tree with a given degree sequence
• Tessellations of random maps of arbitrary genus
• On scaling limits of planar maps with stable face-degrees
• A Boltzmann Approach to Percolation on Random Triangulations
• Scaling limits of random bipartite planar maps with a prescribed degree sequence
• Approximation of solutions of the wave equation driven by a stochastic measure
• Probability Inequalities for Sums of Bounded Random Variables
• Asymptotics of trees with a prescribed degree sequence and applications