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Wasserstein Distance
A fundamental problem in metric algebraic geometry is distance minimization.
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Nonlocal Wasserstein distance: metric and asymptotic properties
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of...
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A note on the Radiant formula and its relations to the sliced Wasserstein distance
In this note, we show that the squared Wasserstein distance can be expressed as the average over the sphere of one dimensional Wasserstein distances....
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Scalable Gromov–Wasserstein Based Comparison of Biological Time Series
A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that...
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Entropic Regularization of Wasserstein Distance Between Infinite-Dimensional Gaussian Measures and Gaussian Processes
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for...
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Coarse Embeddability of Wasserstein Space and the Space of Persistence Diagrams
We prove an equivalence between open questions about the embeddability of the space of persistence diagrams and the space of probability...
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The Cutoff Phenomenon in Wasserstein Distance for Nonlinear Stable Langevin Systems with Small Lévy Noise
This article establishes the cutoff phenomenon in the Wasserstein distance for systems of nonlinear ordinary differential equations with a...
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Quantitative stability of barycenters in the Wasserstein space
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied...
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A kernel formula for regularized Wasserstein proximal operators
We study a class of regularized proximal operators in Wasserstein-2 space. We derive their solutions by kernel integration formulas. We obtain the...
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Topological properties of convex order in Wasserstein metric spaces
Martingale optimal transportation has gained significant attention in mathematical finance due to its applications in pricing and hedging. A key...
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Strong posterior contraction rates via Wasserstein dynamics
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small...
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Subexponential Upper and Lower Bounds in Wasserstein Distance for Markov Processes
In this article, relying on Foster–Lyapunov drift conditions, we establish subexponential upper and lower bounds on the rate of convergence in the
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A comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton–Jacobi equations in the space of probability...
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Entropy-regularized 2-Wasserstein distance between Gaussian measures
Gaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important...
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Absolutely continuous and BV-curves in 1-Wasserstein spaces
We extend the result of Lisini (Calc Var Partial Differ Equ 28:85–120, 2007) on the superposition principle for absolutely continuous curves in p -Wass...
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Exact weights, path metrics, and algebraic Wasserstein distances
We use weights on objects in an abelian category to define what we call a path metric. We introduce three special classes of weight: those compatible...
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On Stein’s Factors for Poisson Approximation in Wasserstein Distance with Nonlinear Transportation Costs
We establish various bounds on the solutions to a Stein equation for Poisson approximation in the Wasserstein distance with nonlinear transportation...