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- Title
FREE TRANSPORT FOR CONVEX POTENTIALS.
- Authors
DABROWSKI, YOANN; GUIONNET, ALICE; SHLYAKHTENKO, DIMA
- Abstract
We construct non-commutative analogs of transport maps among free Gibbs states satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbative in nature and thus can be used to construct transport maps between free Gibbs states associated to potentials which are far from quadratic, i.e., states which are far from the semicircle law. An essential technical ingredient in our approach is the extension of free stochastic analysis to non-commutative spaces of functions based on the Haagerup tensor product.
- Subjects
NONCOMMUTATIVE function spaces; STOCHASTIC analysis; TENSOR products
- Publication
New Zealand Journal of Mathematics, 2021, Vol 52, p259
- ISSN
1171-6096
- Publication type
Article
- DOI
10.53733/102