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Exponential ergodicity of mirror-Langevin diffusions
TLDR
We propose a class of diffusions called Newton-Langevin diffusions and prove that they converge to stationarity exponentially fast with a rate which not only is dimension-free, but also has no dependence on the target distribution. Expand
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Gradient descent algorithms for Bures-Wasserstein barycenters
TLDR
We develop a framework to derive global rates of convergence for both gradient descent and stochastic gradient descent despite the fact that the barycenter functional is not geodesically convex. Expand
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Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show thatExpand
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Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra
TLDR
We propose an algebraic framework for generalized graph Laplacians which unifies the study of resistor networks, the critical group, and adjacency matrices. Expand
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Frog model wakeup time on the complete graph
TLDR
The frog model is a system of random walks where active particles set sleeping particles in motion. Expand
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Fast and Smooth Interpolation on Wasserstein Space.
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us toExpand
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