8 papers
Isometric study of Wasserstein spaces --- the real line
György Pál Gehér, Tamás Titkos, Dániel Virosztek
Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space . It turned out that the case of the rea…
A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means
József Pitrik, Dániel Virosztek
It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positiv…
The metric property of the quantum Jensen-Shannon divergence
Dániel Virosztek
In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum…
Quantum Hellinger distances revisited
József Pitrik, Dániel Virosztek
This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. [Lett. Math. Phys. 109 (2019), 1777-1804] with a particular emphasis on barycenters…
On isometric embeddings of Wasserstein spaces -- the discrete case
György Pál Gehér, Tamás Titkos, Dániel Virosztek
The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space ,…
Maps on probability measures preserving certain distances --- a survey and some new results
Dániel Virosztek
Borel probability measures living on metric spaces are fundamental mathematical objects. There are several meaningful distance functions that make the collection of the probability…