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math.DS2021★ 2 cited
What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
Jianbo Cui, Shu liu, Haomin Zhou
We present a definition of stochastic Hamiltonian process on finite graph via its corresponding density dynamics in Wasserstein manifold. We demonstrate the existence of stochastic…
math.DS2019
Wasserstein Hamiltonian flows
Shui-Nee Chow, Wuchen Li, Haomin Zhou
We establish kinetic Hamiltonian flows in density space embedded with the -Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces…