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Wasserstein Hamiltonian flows

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arxiv 1903.01088 v2 pith:FPMLHNAP submitted 2019-03-04 math.DS math.AP

Shui-Nee Chow , Wuchen Li , Haomin Zhou This is my paper · ORCID
classification math.DSmath.AP
keywords flowshamiltoniandensityequationspacedingerschrwasserstein
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abstract

We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many classical equations, such as Vlasov equation, Schr{\"o}dinger equation and Schr{\"o}dinger bridge problem, can be rewritten as the formalism of Hamiltonian flows in density space.

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  1. Geometric Methods for Stochastic Dynamical Systems

    math.DS 2026-07 conditional novelty 3.0 of 10

    A textbook-style synthesis claiming that the most probable transition path, the Schrödinger bridge, and α-divergence information geodesics are one geometric idea in the space of probability densities.

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