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Entropy-Transport distances between unbalanced metric measure spaces

Abstract:

Inspired by the recent theory of Entropy-Transport problems and by the Ddistance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly different total mass. We provide several explicit examples of such distances, where a prominent role is played by a geodesic metric based on the Hellinger-Kantorovich distance. Moreover, we discuss some limiting cases of the theory, recovering the “pure transport” D-dis...

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Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Springer Publisher's website
Journal:
Probability Theory and Related Fields Journal website
Acceptance date:
2022-07-23
EISSN:
1432-2064
ISSN:
0178-8051
Language:
English
Keywords:
Pubs id:
1135184
Local pid:
pubs:1135184
Deposit date:
2022-07-25

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