Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)

By Andrea Greven, Peter Pfaffelhuber, A. Winter. 2009

197 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b2e2266967ceac13f5b7bbb5399cb7589ffba80c

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Invariance principle for variable speed random walks on trees (2014, methodology): “The Gromov-weak topology on complete and separable metric measure spaces was introduced in [GPW09].”
On the sphericity of scaling limits of random planar quadrangulations (2007, background): “This is not restrictive as Gromov-Hausdorﬀ convergence entails Hausdorﬀ convergence of representative spaces in a common compact space, see for instance [7, Lemma A.1].”
Gromov–Wasserstein Distances and the Metric Approach to Object Matching (2011, background): “5, [50]) For any fixed X ∈ Gw , the map that sends δ ≥ 0 to vδ(X) is non-decreasing, right-continuous and bounded by 1.”
The hull process of the Brownian plane (2014, background): “esnotgive enoughinformationtohandlevolumesofballsorhulls. Itwouldhavebeennecessarytoestablish atypeofGromov-Hausdorﬀ-Prokhorovconvergenceinoursetting,inthespiritoftheworkof Greven,PfaﬀelhuberandWinter[15],whohoweverconsiderthecaseofmetricspacesequipped with a probability measure. This would require ”
CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES (2019, methodology): “Klartag used L(1) optimal transportation methods and the localization technique (going back to the work of Payne–Weinberger Payne and Weinberger [1960] and then further developed in the context of convex geometry byGromov– Milman and Kannan–Lovász–Simonovitz) to provide in Klartag [2017] a new proof”
Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions (2008, unknown): “Let us follow Evans and Winter [9] to introduce a notion of convergence on the space Twt of weight-preserving isometry classes of weighted R-trees.”
The gap between Gromov-vague and Gromov–Hausdorff-vague topology (2014, methodology): “A characterization of Gromov-weak tightness of probability measures of metric finite measures spaces is given in Theorem 3 in [20] (compare also [20, Remark 7.”