English

Partial orders on metric measure spaces

Probability 2016-05-31 v1 Metric Geometry

Abstract

A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new characterization for the Lipschitz order. We will then consider some probabilistic applications. The main importance is given to the study of Fleming-Viot processes with different resampling rates. Besides that application we also consider tree-valued branching processes and two semigroups on metric measure spaces.

Keywords

Cite

@article{arxiv.1605.08989,
  title  = {Partial orders on metric measure spaces},
  author = {Max Grieshammer and Thomas Rippl},
  journal= {arXiv preprint arXiv:1605.08989},
  year   = {2016}
}
R2 v1 2026-06-22T14:12:16.876Z