REVIEW 3 cited by
Optimal transport maps, majorization, and log-subharmonic measures
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous phenomenon holds on the level of the trace: The trace of the derivative of the optimal transport map between a log-subharmonic measure and a strongly log-concave measure is bounded. We show that this trace bound has a number of consequences pertaining to volume-contracting transport maps, majorization and its monotonicity along Wasserstein geodesics, growth estimates of log-subharmonic functions, the Wehrl conjecture for Glauber states, and two-dimensional Coulomb gases. We also discuss volume-contraction properties for the Kim-Milman transport map
Forward citations
Cited by 3 Pith papers
-
Optimal transport of signed measures: existence, uniqueness and fractal structure part I: the separated-support case research announcement, with a numerical validation report
Existence and uniqueness of optimal transport maps for signed measures are proved, preserving Hausdorff dimension and Ahlfors regularity of fractal sets via coupled Monge-Ampere equations and adaptive regularization.
-
Optimal transport of signed measures: existence, uniqueness and fractal structure part I: the separated-support case research announcement, with a numerical validation report
A research announcement (with full proofs and the advertised numerical report missing) claims existence/uniqueness and Hausdorff-dimension preservation for optimal transport of signed measures with fractal singular co...
-
Optimal transport of signed measures: existence, uniqueness and fractal structure part I: the separated-support case research announcement, with a numerical validation report
The paper proves existence and uniqueness of optimal transport maps for signed measures with fractal singular parts, derives coupled Monge-Ampere equations, and shows the maps preserve Hausdorff dimension and Ahlfors ...
Discussion (0). Sign in to comment.