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- W4313483412 abstract "We investigate the quadratic Schrodinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schrodinger potentials under mild assumptions on the marginals that are substantially weaker than log-concavity. We deduce from these estimates that Schrodinger bridges satisfy a logarithmic Sobolev inequality on the product space. Our proof strategy is based on a second order analysis of coupling by reflection on the characteristics of the Hamilton-Jacobi-Bellman equation that reveals the existence of new classes of invariant functions for the corresponding flow." @default.
- W4313483412 created "2023-01-06" @default.
- W4313483412 creator A5035963850 @default.
- W4313483412 date "2022-12-30" @default.
- W4313483412 modified "2023-09-30" @default.
- W4313483412 title "Weak semiconvexity estimates for Schrodinger potentials and logarithmic Sobolev inequality for Schrodinger bridges" @default.
- W4313483412 doi "https://doi.org/10.48550/arxiv.2301.00083" @default.
- W4313483412 hasPublicationYear "2022" @default.
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