2 citations · 4 across the 6 of their papers we have counts for
6 papers
Gradient flow structure for some nonlocal diffusion equations
Andrew Warren
We study ``nonlocal diffusion equations'' of the form \[ \partial_{t}\frac{dρ_{t}}{dπ}(x)+\int_{X}\left(\frac{dρ_{t}}{dπ}(x)-\frac{dρ_{t}}{dπ}(y)\right)η(x,y)dπ(y)=0\qquad(\dagger)…
Ultralimits of Wasserstein spaces and metric measure spaces with Ricci curvature bounded from below
Andrew Warren
We investigate the stability of the Wasserstein distance, a metric structure on the space of probability measures arising from the theory of optimal transport, under metric ultrali…
Nonlocal Wasserstein Distance: Metric and Asymptotic Properties
Dejan Slepčev, Andrew Warren
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 probability measures, where path…
Fluctuation bounds for ergodic averages of amenable groups
Andrew Warren
We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable group…
Wasserstein Conditional Independence Testing
Andrew Warren
We introduce a test for the conditional independence of random variables and given a random variable , specifically by sampling from the joint distribution , bi…
Fluctuation bounds for ergodic averages of amenable groups on uniformly convex Banach spaces
Andrew Warren
We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable group…