The enriched CREM free energy in the weak correlation regime equals the maximum over one parameter of a simple formula involving t, the path q, and ln 2, and this value is independent of the covariance function A.
Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations
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It is well known that when the nonlinearity is convex, the Hamilton-Jacobi PDE admits a unique semi-convex weak solution, which is the viscosity solution. In this paper, motivated by problems arising from spin glasses, we show that if the Hamilton-Jacobi PDE with strictly convex nonlinearity and regular enough initial condition admits a semi-concave weak solution, then this solution is the viscosity solution.
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The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime
The enriched CREM free energy in the weak correlation regime equals the maximum over one parameter of a simple formula involving t, the path q, and ln 2, and this value is independent of the covariance function A.