Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability

Stability of Schrödinger potentials and convergence of Sinkhorn’s algorithm

(2023) Marcel Nutz et al.   ANNALS OF PROBABILITY

Convergence rate of general entropic optimal transport costs

(2023) Guillaume Carlier et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

A Generalization of Costa’s Entropy Power Inequality

(2022) Luca Tamanini   IEEE TRANSACTIONS ON INFORMATION THEORY

A formula for the time derivative of the entropic cost and applications

(2021) Giovanni Conforti et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Second order differentiation formula on RCD*$(K,N)$ spaces

(2021) Nicola Gigli et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Entropic optimal transport: convergence of potentials

(2021) Marcel Nutz et al.   PROBABILITY THEORY AND RELATED FIELDS

Dynamical aspects of the generalized Schrödinger problem via Otto calculus – A heuristic point of view

(2020) Ivan Gentil et al.   REVISTA MATEMATICA IBEROAMERICANA

A Differential Approach to the Multi-Marginal Schrödinger System

(2020) Guillaume Carlier et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities

(2020) Julio Backhoff et al.   PROBABILITY THEORY AND RELATED FIELDS

Benamou–Brenier and duality formulas for the entropic cost on $${\textsf {RCD}}^*(K,N)$$ RCD ∗ ( K , N ) spaces

(2019) Nicola Gigli et al.   PROBABILITY THEORY AND RELATED FIELDS

A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost

(2018) Giovanni Conforti   PROBABILITY THEORY AND RELATED FIELDS

Hamilton’s gradient estimates and a monotonicity formula for heat flows on metric measure spaces

(2016) Renjin Jiang et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

From large deviations to Wasserstein gradient flows in multiple dimensions

(2015) Matthias Erbar et al.   ELECTRONIC COMMUNICATIONS IN PROBABILITY

Heat Kernel Bounds on Metric Measure Spaces and Some Applications

(2015) Renjin Jiang et al.   POTENTIAL ANALYSIS

The Monge–Ampère equation and its link to optimal transportation

(2014) Guido De Philippis et al.   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

Metric measure spaces with Riemannian Ricci curvature bounded from below

(2014) Luigi Ambrosio et al.   DUKE MATHEMATICAL JOURNAL

A survey of the Schrödinger problem and some of its connections with optimal transport

(2013) Christian Léonard   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

(2013) Luigi Ambrosio et al.   INVENTIONES MATHEMATICAE

Equivalent semigroup properties for the curvature-dimension condition

(2011) Feng-Yu Wang   BULLETIN DES SCIENCES MATHEMATIQUES

From a Large-Deviations Principle to the Wasserstein Gradient Flow: A New Micro-Macro Passage

(2011) Stefan Adams et al.   COMMUNICATIONS IN MATHEMATICAL PHYSICS

From the Schrödinger problem to the Monge–Kantorovich problem

(2011) Christian Léonard   JOURNAL OF FUNCTIONAL ANALYSIS

Local semiconvexity of Kantorovich potentials on non-compact manifolds

(2010) Alessio Figalli et al.   ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS

Mass Transport and Variants of the Logarithmic Sobolev Inequality

(2008) Franck Barthe et al.   JOURNAL OF GEOMETRIC ANALYSIS