Optimal transport between random measures
Optimal transport between random measures
View/Type of Scholarly Publication
DissertationDate of Exam
11.06.2012Date of Publication
17.07.2012Advisor
Sturm, Karl-TheodorCo-Referee
Ferrari, Patrik L.Metadata
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Abstract
We study couplings q• of two equivariant random measures λ• and μ• on a Riemannian manifold (M,d,m). Given a cost function we ask for minimizers of the mean transportation cost per volume. In case the minimal/optimal cost is finite and λω ≪ m we prove that there is a unique equivariant coupling minimizing the mean transportation cost per volume. Moreover, the optimal coupling is induced by a transportation map, q•=(id,T)*λ•. We show that the optimal transportation map can be approximated by solutions to classical optimal transportation problems on bounded regions. In case of Lp - cost the optimal transportation cost per volume defines a metric on the space of equivariant random measure with unit intensity.
Subjects
Poisson process, optimal coupling, random measures, transport map, Laguerre tessellation
Classification (DDC)
510 MathematikHuesmann, Martin Otto Josef: Optimal transport between random measures. - Bonn, 2012. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29072
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29072
@phdthesis{handle:20.500.11811/5335,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29072,
author = {{Martin Otto Josef Huesmann}},
title = {Optimal transport between random measures},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = jul,
note = {We study couplings q• of two equivariant random measures λ• and μ• on a Riemannian manifold (M,d,m). Given a cost function we ask for minimizers of the mean transportation cost per volume. In case the minimal/optimal cost is finite and λω ≪ m we prove that there is a unique equivariant coupling minimizing the mean transportation cost per volume. Moreover, the optimal coupling is induced by a transportation map, q•=(id,T)*λ•. We show that the optimal transportation map can be approximated by solutions to classical optimal transportation problems on bounded regions. In case of Lp - cost the optimal transportation cost per volume defines a metric on the space of equivariant random measure with unit intensity.},
url = {https://hdl.handle.net/20.500.11811/5335}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29072,
author = {{Martin Otto Josef Huesmann}},
title = {Optimal transport between random measures},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = jul,
note = {We study couplings q• of two equivariant random measures λ• and μ• on a Riemannian manifold (M,d,m). Given a cost function we ask for minimizers of the mean transportation cost per volume. In case the minimal/optimal cost is finite and λω ≪ m we prove that there is a unique equivariant coupling minimizing the mean transportation cost per volume. Moreover, the optimal coupling is induced by a transportation map, q•=(id,T)*λ•. We show that the optimal transportation map can be approximated by solutions to classical optimal transportation problems on bounded regions. In case of Lp - cost the optimal transportation cost per volume defines a metric on the space of equivariant random measure with unit intensity.},
url = {https://hdl.handle.net/20.500.11811/5335}
}
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