DC Field | Value | Language |
---|---|---|
dc.contributor.author | Gangbo, Wilfrid | ko |
dc.contributor.author | Jekel, David | ko |
dc.contributor.author | Nam, Kyeongsik | ko |
dc.contributor.author | Shlyakhtenko, Dimitri | ko |
dc.date.accessioned | 2022-11-18T03:00:13Z | - |
dc.date.available | 2022-11-18T03:00:13Z | - |
dc.date.created | 2022-09-19 | - |
dc.date.created | 2022-09-19 | - |
dc.date.created | 2022-09-19 | - |
dc.date.issued | 2022-12 | - |
dc.identifier.citation | COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.396, no.3, pp.903 - 981 | - |
dc.identifier.issn | 0010-3616 | - |
dc.identifier.uri | http://hdl.handle.net/10203/299924 | - |
dc.description.abstract | We study the free probabilistic analog of optimal couplings for the quadratic cost, where classical probability spaces are replaced by tracial von Neumann algebras, and probability measures on R-m are replaced by non-commutative laws of m-tuples. We prove an analog of the Monge-Kantorovich duality which characterizes optimal couplings of non-commutative laws with respect to Biane and Voiculescu's non-commutative L-2-Wasserstein distance using a new type of convex functions. As a consequence, we show that if (X, Y) is a pair of optimally coupled m-tuples of non-commutative random variables in a tracial W*-algebra A, then W*((1 - t)X + tY) = W* (X, Y) for all t is an element of (0, 1). Finally, we illustrate the subtleties of non-commutative optimal couplings through connections with results in quantum information theory and operator algebras. For instance, two non-commutative laws that can be realized in finite-dimensional algebras may still require an infinite-dimensional algebra to optimally couple. Moreover, the space of non-commutative laws of m-tuples is not separable with respect to the Wasserstein distance for m > 1. | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.title | Duality for Optimal Couplings in Free Probability | - |
dc.type | Article | - |
dc.identifier.wosid | 000852927400003 | - |
dc.identifier.scopusid | 2-s2.0-85137929864 | - |
dc.type.rims | ART | - |
dc.citation.volume | 396 | - |
dc.citation.issue | 3 | - |
dc.citation.beginningpage | 903 | - |
dc.citation.endingpage | 981 | - |
dc.citation.publicationname | COMMUNICATIONS IN MATHEMATICAL PHYSICS | - |
dc.identifier.doi | 10.1007/s00220-022-04480-0 | - |
dc.contributor.localauthor | Nam, Kyeongsik | - |
dc.contributor.nonIdAuthor | Gangbo, Wilfrid | - |
dc.contributor.nonIdAuthor | Jekel, David | - |
dc.contributor.nonIdAuthor | Shlyakhtenko, Dimitri | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | HAMILTON-JACOBI EQUATIONS | - |
dc.subject.keywordPlus | TRANSPORTATION COST INEQUALITIES | - |
dc.subject.keywordPlus | FISHERS INFORMATION MEASURE | - |
dc.subject.keywordPlus | INFINITE DIMENSIONS | - |
dc.subject.keywordPlus | ENTROPY | - |
dc.subject.keywordPlus | ANALOGS | - |
dc.subject.keywordPlus | CLASSIFICATION | - |
dc.subject.keywordPlus | AMENABILITY | - |
dc.subject.keywordPlus | EMBEDDINGS | - |
dc.subject.keywordPlus | UNITARY | - |
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