Hamilton–Jacobi equations for mean-field disordered systems
Jean-Christophe Mourrat
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.
Topics & Concepts
Hamilton–Jacobi equationMathematicsTerm (time)Viscosity solutionApplied mathematicsLimit (mathematics)Scale (ratio)Matrix (chemical analysis)Rank (graph theory)Mean field theoryMathematical analysisMathematical physicsPhysicsCombinatoricsQuantum mechanicsMaterials scienceComposite materialTheoretical and Computational PhysicsRandom Matrices and ApplicationsQuantum many-body systems