Hamilton-Jacobi equations for mean-field disordered systems

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.

29 pages, v2: tensor case added

References in corpus (1)

• Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula

Cited by in corpus (4)

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