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.
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}
}