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Weak KAM theory for action minimizing random walks

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Abstract

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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Acknowledgements

The author is supported by JSPS Grant-in-aid for Young Scientists #18K13443.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Kohei Soga

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  1. Kohei Soga
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Correspondence to Kohei Soga.

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Communicated by Y. Giga.

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Soga, K. Weak KAM theory for action minimizing random walks. Calc. Var. 60, 179 (2021). https://doi.org/10.1007/s00526-021-02025-2

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