An axiomatic characterization of the Brownian map
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Publication:2660431
DOI10.5802/jep.155zbMath1478.60043arXiv1506.03806OpenAlexW3135001697MaRDI QIDQ2660431
Publication date: 30 March 2021
Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.03806
Geometric probability and stochastic geometry (60D05) Quantization of the gravitational field (83C45)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Imaginary geometry. I: Interacting SLEs
- The hull process of the Brownian plane
- Conformal weldings of random surfaces: SLE and the quantum gravity zipper
- Imaginary geometry. III: Reversibility of \(\mathrm{SLE}_\kappa\) for \(\kappa \in (4,8)\)
- Uniqueness and universality of the Brownian map
- The Brownian map is the scaling limit of uniform random plane quadrangulations
- Addendum: Commentary for ``On planarity of compact, locally connected, metric spaces
- Quantum Loewner evolution
- Quantum gravity and inventory accumulation
- Scaling limits for the peeling process on random maps
- Compact Brownian surfaces. I: Brownian disks
- Geodesics in large planar maps and in the Brownian map
- Imaginary geometry. II: Reversibility of \(\operatorname{SLE}_{\kappa}(\rho_{1};\rho_{2})\) for \(\kappa\in(0,4)\)
- Equivalence of Gromov-Prohorov- and Gromov's \(\underline{\square}_\lambda\)-metric on the space of metric measure spaces
- The continuum random tree. I
- Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees)
- Bijective counting of tree-rooted maps and shuffles of parenthesis systems
- Limit of normalized quadrangulations: the Brownian map
- Proof(s) of the Lamperti representation of continuous-state branching processes
- Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere
- On the sphericity of scaling limits of random planar quadrangulations
- On the re-rooting invariance property of Lévy trees
- A bijective census of nonseparable planar maps
- Branching processes in Lévy processes: The exploration process
- Conditionings and path decompositions for Lévy processes
- Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
- A large deviation principle for the Brownian snake
- Uniform infinite planar triangulations
- Growth and percolation on the uniform infinite planar triangulation
- Random planar lattices and integrated superBrownian excursion
- Construction of non-critical string field theory by transfer matrix formalism in dynamical triangulation
- Enumeration of planar constellations
- Scaling limits of loop-erased random walks and uniform spanning trees
- Martingales in self-similar growth-fragmentations and their connections with random planar maps
- Excursion theory for Brownian motion indexed by the Brownian tree
- Subordination of trees and the Brownian map
- Imaginary geometry. IV: Interior rays, whole-plane reversibility, and space-filling trees
- Brownian disks and the Brownian snake
- Random planar maps and growth-fragmentations
- Probabilistic and fractal aspects of Lévy trees
- Conformal loop ensembles: the Markovian characterization and the loop-soup construction
- The Brownian cactus. I: Scaling limits of discrete cactuses
- Liouville quantum gravity and the Brownian map. I: The \(\text{QLE}(8/3,0)\) metric
- Metric gluing of Brownian and \(\sqrt{8/3}\)-Liouville quantum gravity surfaces
- Liouville quantum gravity spheres as matings of finite-diameter trees
- The continuum random tree. III
- Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology
- Introductory lectures on fluctuations of Lévy processes with applications.
- Random stable looptrees
- A glimpse of the conformal structure of random planar maps
- Regular convergence
- Random sampling of large planar maps and convex polyhedra
- THE BROWNIAN MAP: A UNIVERSAL LIMIT FOR RANDOM PLANAR MAPS
- Planar Maps are Well Labeled Trees
- 3-connected planar spaces uniquely embed in the sphere
- A Census of Planar Triangulations
- Constructions of local time for a Markov process
- Random Walks and Quantum Gravity in Two Dimensions
- Pasting Together Julia Sets: A Worked Out Example of Mating
- Random geometry on the sphere
- Scaling limits of random trees and planar maps
- On the Enumeration of Tree-Rooted Maps
- On the enumeration of planar maps
- Stochastic branching processes with continuous state space
- Continuous state branching processes
- Probability
- Optimal Transport
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