Maps on probability measures preserving certain distances - a survey and some new results
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 isometr...
Elmentve itt :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2018
|
| Sorozat: | Acta scientiarum mathematicarum
84 No. 1-2 |
| Kulcsszavak: | Izometria, Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/55804 |
| LEADER | 01572nab a2200217 i 4500 | ||
|---|---|---|---|
| 001 | acta55804 | ||
| 005 | 20260219155405.0 | ||
| 008 | 181110s2018 hu o 000 eng d | ||
| 022 | |a 0001-6969 | ||
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Virosztek Dániel | |
| 245 | 1 | 0 | |a Maps on probability measures preserving certain distances - a survey and some new results |h [elektronikus dokumentum] / |c Virosztek Dániel |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2018 | ||
| 300 | |a 65-80 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 84 No. 1-2 | |
| 520 | 3 | |a 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 Wp 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Izometria, Matematika | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/55804/1/math_084_numb_001-002_065-080.pdf |z Dokumentum-elérés |