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.
Weak-Strong Uniqueness Principle for Hamilton-Jacobi Equations
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We show that if a Hamilton-Jacobi equation admits a differentiable solution whose gradient is Lipschitz, then this solution is the unique semi-concave weak solution. Our result does not rely on any convexity (nor concavity) assumptions on the initial condition or the nonlinearity, and can therefore be utilized in contexts where the viscosity solution admits no standard variational representation.
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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.