Sinkhorn iterations converge to a Wasserstein mirror gradient flow (the Sinkhorn flow) as regularization epsilon goes to zero with iterations scaled as 1/epsilon.
Villani, Optimal transportation, dissipative PDE’s and func- tional inequalities , Unpublished lecture notes
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Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm
Sinkhorn iterations converge to a Wasserstein mirror gradient flow (the Sinkhorn flow) as regularization epsilon goes to zero with iterations scaled as 1/epsilon.