Optimal transport began as the problem of how to efficiently redistribute goods between
production and consumers and evolved into a far-reaching geometric variational framework …

In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of
large deviations of the empirical distribution). Schrödinger's problem represents an early …

We take a new look at the relation between the optimal transport problem and the
Schrödinger bridge problem from a stochastic control perspective. Our aim is to highlight …

We consider the problem of steering a linear dynamical system with complete state
observation from an initial Gaussian distribution in state-space to a final one with minimum …

We introduce an optimal mass transport framework on the space of Gaussian mixture
models. These models are widely used in statistical inference. Specifically, we treat the …

We study multi-marginal optimal transport problems from a probabilistic graphical model
perspective. We point out an elegant connection between the two when the underlying cost …

During recent decades, there has been a substantial development in optimal mass transport
theory and methods. In this work, we consider multi-marginal problems wherein only partial …

Monge--Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the
space of positive densities---it quantifies the cost of transporting a mass distribution into …

In this article, we study the Schrödinger bridge problem (SBP) with nonlinear prior dynamics.
In control-theoretic language, this is a problem of minimum effort steering of a given joint …

Consider a reference Markov process with initial distribution $\pi_ {0} $ and transition
kernels $\{M_ {t}\} _ {t\in [1: T]} $, for some $ T\in\mathbb {N} $. Assume that you are given …