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We study generalizations of the Schr\"odinger problem in statistical mechanics in two directions: when the density is constrained at more than two times, and when the joint law of the initial and final positions for the particles is prescribed.
Über die Umkehrung der Naturgesetze
E. Schrödinger · 1931
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Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique
E. Schrödinger · 1932
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Measure Theory
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An automorphism of product measures
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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Diagonal equivalence to matrices with prescribed row and column sums
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I I -divergence geometry of probability distributions and minimization problems
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Claude Dellacherie and Paul-André Meyer · 1978
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Sur la régularité des trajectoires des martingales à deux indices
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Large deviations from the McKean-Vlasov limit for weakly interacting diffusions
D.A. Dawson and J. Gärtner · 1987
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Random fields and diffusion processes, in École d’été de Probabilités de Saint-Flour XV-XVII-1985-87
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The least action principle and the related concept of generalized flows for incompressible perfect fluids
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T. Mikami · 2004
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Probability and statistics, Vol. 2
D. Dacunha-Castelle and M. Duflo · 2012
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From the Schrödinger problem to the Monge–Kantorovich problem
Christian Léonard · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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Some properties of path measures
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A survey of the Schrödinger problem and some of its connections with optimal transport
C. Léonard · 2014
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Closedness of sum spaces and the generalized Schrödinger problem
L. Rüschendorf and W. Thomsen · 1998
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Minimizers of energy functionals
C. Léonard · 2001
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An entropic interpolation problem for incompressible viscid fluids
M. Arnaudon, A.B. Cruzeiro, C. Léonard, and J.-C. Zambrini
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On the existence of a scalar pressure field in the brödinger problem
A. Baradat
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Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
A. Baradat and L. Monsaingeon
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Reciprocal processes. A measure-theoretical point of view
C. Léonard, S. Rœlly, and J-C. Zambrini · 2014
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Iterative Bregman projections for regularized transportation problems
J-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré · 2015
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