A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
From MaRDI portal
Publication:388854
DOI10.1214/EJP.v18-2116zbMath1285.60004arXiv1202.5464OpenAlexW1699290243MaRDI QIDQ388854
Romain Abraham, Jean-François Delmas, Patrick Hoscheit
Publication date: 17 January 2014
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1202.5464
Probability measures on topological spaces (60B05) Random graphs (graph-theoretic aspects) (05C80) Complete metric spaces (54E50)
Related Items (66)
Random tree-weighted graphs ⋮ Mutations on a random binary tree with measured boundary ⋮ On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees ⋮ Reversal property of the Brownian tree ⋮ Geodesic stars in random geometry ⋮ Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows ⋮ The hyperbolic Brownian plane ⋮ The Brownian disk viewed from a boundary point ⋮ Metrization of the Gromov-Hausdorff (-Prokhorov) topology for boundedly-compact metric spaces ⋮ Asymptotic properties of random unlabelled block-weighted graphs ⋮ Infinite stable looptrees ⋮ Liouville quantum gravity with matter central charge in (1, 25): a probabilistic approach ⋮ Gromov-Hausdorff-Prokhorov convergence of vertex cut-trees of \(n\)-leaf Galton-Watson trees ⋮ Random gluing of metric spaces ⋮ The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces ⋮ Moduli spaces of compact \(\mathrm{RCD}(0,N)\)-structures ⋮ Convergence of blanket times for sequences of random walks on critical random graphs ⋮ The Brownian Web as a random \(\mathbb{R} \)-tree ⋮ Scaling limit of linearly edge-reinforced random walks on critical Galton-Watson trees ⋮ Growing random graphs with a preferential attachment structure ⋮ The Minkowski content measure for the Liouville quantum gravity metric ⋮ The SLE loop via conformal welding of quantum disks ⋮ Scaling Limits of Markov-Branching Trees and Applications ⋮ Scaling limits of \(k\)-ary growing trees ⋮ Convergence of bi-measure \(\mathbb{R}\)-trees and the pruning process ⋮ A unified framework for generalizing the Gromov-Hausdorff metric ⋮ Geometry of the minimal spanning tree in the heavy-tailed regime: new universality classes ⋮ A recursive distributional equation for the stable tree ⋮ Enhancing non-melonic triangulations: a tensor model mixing melonic and planar maps ⋮ On the average L^q-dimensions of typical measures belonging to the Gromov–Hausdorff–Prohoroff space. The limiting cases: q = 1 and q = ∞ ⋮ The forest associated with the record process on a Lévy tree ⋮ Heavy subtrees of Galton-Watson trees with an application to Apollonian networks ⋮ Scaling Limits of Random Trees and Random Graphs ⋮ Scaling limit of dynamical percolation on critical Erdős-Rényi random graphs ⋮ A tree-valued Markov process associated with an admissible family of branching mechanisms ⋮ An invariance principle for branching diffusions in bounded domains ⋮ Small trees in supercritical random forests ⋮ On trees invariant under edge contraction ⋮ Critical random graphs and the differential equations technique ⋮ Invariance principles for random walks in random environment on trees ⋮ The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs ⋮ Scaling limits for some random trees constructed inhomogeneously ⋮ Continuum limit of critical inhomogeneous random graphs ⋮ Exit times for an increasing Lévy tree-valued process ⋮ The random conductance model with heavy tails on nested fractal graphs ⋮ On the average \(L^q\)-dimensions of typical measures belonging to the Gromov-Hausdorff-Prohoroff space ⋮ SLE as a mating of trees in Euclidean geometry ⋮ Geometry of the minimal spanning tree of a random 3-regular graph ⋮ Scaling limits of multi-type Markov branching trees ⋮ The gap between Gromov-Vague and Gromov-Hausdorff-vague topology ⋮ Brownian motion on stable looptrees ⋮ Self-similar real trees defined as fixed points and their geometric properties ⋮ Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense ⋮ Speeding up non-Markovian first-passage percolation with a few extra edges ⋮ Spine representations for non-compact models of random geometry ⋮ Simply Generated Unrooted Plane Trees ⋮ On the geometry of irreversible metric-measure spaces: convergence, stability and analytic aspects ⋮ Limits of multiplicative inhomogeneous random graphs and Lévy trees: limit theorems ⋮ Scaling limits of the three-dimensional uniform spanning tree and associated random walk ⋮ Global regime for general additive functionals of conditioned Bienaymé-Galton-Watson trees ⋮ Scaling limits of tree-valued branching random walks ⋮ Scaling limits for a family of unrooted trees ⋮ Scaling limit of random forests with prescribed degree sequences ⋮ The volume measure of the Brownian sphere is a Hausdorff measure ⋮ Inverting the cut-tree transform ⋮ Exact simulation of the genealogical tree for a stationary branching population and application to the asymptotics of its total length
This page was built for publication: A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
