Related papers: The Poisson transport map
We develop a new method based on Caffarelli's contraction theorem in optimal transport to obtain sharp and uniform modulus of continuity estimates for $\beta$-Dyson Brownian motions with $\beta \geq 2$. Our method extends to a large class…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave…
We extend the classical regularity theory of optimal transport to non-optimal transport maps generated by heat flow for perturbations of Gaussian measures. Considering probability measures of the form $d\mu(x) = \exp\left(-\frac{|x|^2}{2} +…
In this paper, we give necessary and sufficient conditions for Talagrand's like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimension-free concentration of…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on $\RR^n$ and different classes of measures: Gaussian measures on $\RR^n$, symmetric Bernoulli and symmetric uniform probability measures on…
An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note,…
Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…
Reverse H\"{o}lder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev inequality can be used to derive reverse H\"{o}lder…
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the…
If the cost function is not too far from the Euclidean cost, then the optimal map transporting Gaussians restricted to a ball will be regular. \ Similarly, given any cost function which is smooth in a neighborhood of two points on a…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…