A Universal Lower Bound for the Complexity of Gaussian-Divisible Spin Glasses

Abstract: We consider a variant of the spherical mixed spin glass model with non-Gaussian disorder. Specifically, we replace the usual standard Gaussian interaction coefficients with Gaussian-divisible ones, meaning that each coefficient can be expressed as the sum of a standard Gaussian random variable and an independent, non-Gaussian random variable. We show that the annealed complexity of this model is at least the annealed complexity of the standard Gaussian model, if the non-Gaussian part is centered and subexponential.