Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes

170 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (2021, background): “Under mild assumptions, the static SB problem can be seen as an entropy-regularized optimal transport problem since (10) is equivalent to Song and Ermon (2019), then k which induces a quadratic cost and Mikami (2004) showed that π s ,(cid:63) → π (cid:63) W weakly and 2 σ 2 KL( π s ,(cid:63) | p 0 ,”
A formula for the time derivative of the entropic cost and applications (2019, background): “8), see for instance [22, 25] for Γ-convergence results.”
Second order differentiation formula on RCD*$(K,N)$ spaces (2018, background): “The first connections between Schrödinger equations and optimal transport have been obtained by Mikami in [45] for the quadratic cost on Rd; later Mikami-Thieullen [46] showed that a link persists even for more general cost functions.”
Stability of entropic optimal transport and Schrödinger bridges (2021, background): “Starting with [36, 37], a number of works examine the degenerate asymptotic ε → 0 where the limiting problem is classical optimal transport.”
A survey of the Schr\"odinger problem and some of its connections with optimal transport (2013, background): “Mikami in [Mik04] with a stochastic control approach which differs from what is presented below.”