Hamilton-Jacobi equations for mean-field disordered systems

2018/11/04 by Mourrat, Jean-Christophe · 1 citation
#82B44 #82D30 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR)

paper · doi:10.48550/arxiv.1811.01432

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.

Cited by

• The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime

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