On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
Motivated by the occurrence in rate functions of time-dependent large-deviation principles,
we study a class of non-negative functions ℒ that induce a flow, given by ℒ (ρ t, ρ ̇ t)= 0 …
we study a class of non-negative functions ℒ that induce a flow, given by ℒ (ρ t, ρ ̇ t)= 0 …
Entropic optimal transport: Geometry and large deviations
We study the convergence of entropically regularized optimal transport to optimal transport.
The main result is concerned with the convergence of the associated optimizers and takes …
The main result is concerned with the convergence of the associated optimizers and takes …
A formula for the time derivative of the entropic cost and applications
G Conforti, L Tamanini - Journal of Functional Analysis, 2021 - Elsevier
In the recent years the Schrödinger problem has gained a lot of attention because of the
connection, in the small-noise regime, with the Monge-Kantorovich optimal transport …
connection, in the small-noise regime, with the Monge-Kantorovich optimal transport …
Convergence rates for regularized optimal transport via quantization
S Eckstein, M Nutz - Mathematics of Operations Research, 2024 - pubsonline.informs.org
We study the convergence of divergence-regularized optimal transport as the regularization
parameter vanishes. Sharp rates for general divergences including relative entropy or Lp …
parameter vanishes. Sharp rates for general divergences including relative entropy or Lp …
Large deviations and gradient flows
S Adams, N Dirr, M Peletier… - … Transactions of the …, 2013 - royalsocietypublishing.org
In recent work we uncovered intriguing connections between Otto's characterization of
diffusion as an entropic gradient flow on the one hand and large-deviation principles …
diffusion as an entropic gradient flow on the one hand and large-deviation principles …
A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility
Abstract Onsager's 1931 “reciprocity relations” result connects microscopic time reversibility
with a symmetry property of corresponding macroscopic evolution equations. Among the …
with a symmetry property of corresponding macroscopic evolution equations. Among the …
Doubly regularized entropic Wasserstein barycenters
L Chizat - arXiv preprint arXiv:2303.11844, 2023 - arxiv.org
We study a general formulation of regularized Wasserstein barycenters that enjoys favorable
regularity, approximation, stability and (grid-free) optimization properties. This barycenter is …
regularity, approximation, stability and (grid-free) optimization properties. This barycenter is …
Variational modelling: Energies, gradient flows, and large deviations
MA Peletier - arXiv preprint arXiv:1402.1990, 2014 - arxiv.org
These are lecture notes for various Summer and Winter schools that I have given. The notes
describe the methodology called Variational Modelling, and focus on the application to the …
describe the methodology called Variational Modelling, and focus on the application to the …
Nearly tight convergence bounds for semi-discrete entropic optimal transport
A Delalande - International Conference on Artificial …, 2022 - proceedings.mlr.press
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic
semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of …
semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of …
On the difference between entropic cost and the optimal transport cost
S Pal - arXiv preprint arXiv:1905.12206, 2019 - arxiv.org
Consider the Monge-Kantorovich problem of transporting densities $\rho_0 $ to $\rho_1 $
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …