# 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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