From a Large-Deviations Principle to the Wasserstein Gradient Flow: A New Micro-Macro Passage

@article{Adams2010FromAL,
  title={From a Large-Deviations Principle to the Wasserstein Gradient Flow: A New Micro-Macro Passage},
  author={Stefan Adams and Nicolas Dirr and Mark A. Peletier and Johannes Zimmer},
  journal={Communications in Mathematical Physics},
  year={2010},
  volume={307},
  pages={791-815}
}
We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional Jh characterizes the behaviour of the particle system at t = h in terms of the initial distribution at t = 0. For the diffusion equation, a single step in the time-discretized entropy-Wasserstein gradient flow is characterized by the minimization of a functional Kh. We establish a new… 

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