Hamilton–Jacobi equations for mean-field disordered systems
Annales Henri Lebesgue, Volume 4 (2021) , pp. 453-484.


Keywordsspin glass, statistical inference, Hamilton–Jacobi equation


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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