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An infinite-dimensional weak KAM theory via random variables

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  • We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on $\mathbb{R}$.
    Mathematics Subject Classification: Primary: 37K05, 37K55; Secondary: 49L20, 49L25.

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