Author(s):

Virosztek, Daniel

Article Title: 
Maps on probability measures preserving certain distances  a survey and some new results

Affiliation 
IST Austria 
Abstract: 
Borel probability measures living on metric spaces are fundamental
mathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere.

Keywords: 
Wasserstein isometries; unit sphere

Journal Title:

Acta Scientiarum Mathematicarum (Szeged)

Volume: 
84

Issue 
12

ISSN:

00016969

Publisher:

Bolyai Institute

Date Published:

20180604

Start Page: 
65

End Page:

80

Sponsor: 
The author was supported by the ISTFELLOW program of the Institute of Science and Technol ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).

URL: 

DOI: 
10.14232/actasm018753y

Open access: 
yes (repository) 