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arXiv · 1811.01432

Hamilton-Jacobi equations for mean-field disordered systems

Jean-Christophe Mourrat
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Abstract

We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix. We compute the large-scale limit of the free energy by showing that it satisfies an approximate Hamilton-Jacobi equation with asymptotically vanishing viscosity parameter and error term.

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Jean-Christophe Mourrat. 2018-11-04. Hamilton-Jacobi equations for mean-field disordered systems. https://arxiv.org/abs/1811.01432

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