67 citations · 165 across the 28 of their papers we have counts for
38 papers
Mirror Langevin diffusions: Convergence rates and Markov chain approximations
Benjamin Capdeville, Young-Heon Kim, Soumik Pal
Given a strongly convex function , equip with a Riemannian metric given by the Hessian . This is a so-called Hessian manifold. Given a probability density …
Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm
Nabarun Deb, Young-Heon Kim, Soumik Pal +1
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges…
Backward and Forward Wasserstein Projections in Stochastic Order
Young-Heon Kim, Yuan Long Ruan
We study metric projections onto cones in the Wasserstein space of probability measures, defined by stochastic orders. Dualities for backward and forward projections are establishe…
The Stefan problem and free targets of optimal Brownian martingale transport
Inwon C. Kim, Young-Heon Kim
We formulate and solve a free target optimal Brownian stopping problem from a given distribution while the target distribution is free and is conditioned to satisfy a given density…
Towards a mathematical theory of trajectory inference
Hugo Lavenant, Stephen Zhang, Young-Heon Kim +1
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis o…
Hidden convexity in a problem of nonlinear elasticity
Nassif Ghoussoub, Young-Heon Kim, Hugo Lavenant +1
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a glo…