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Weak KAM theory for action minimizing random walks
Kohei Soga · 2020-10-23 · via math.PR updates on arXiv.org

We introduce a class of controlled random walks on a grid in $\mathbb{T}^d$ and investigate global properties of action minimizing random walks for a certain action functional together with Hamilton-Jacobi equations on the grid. This yields an analogue of weak KAM theory, which recovers a part of original weak KAM theory through the hyperbolic scaling limit.

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