Exponential growth of random determinants beyond invariance

We give simple criteria to identify the exponential order of magnitude absolute value determinant for wide classes random matrix models, not requiring assumption invariance. These include Gaussian matrices with covariance profiles, Wigner and subexponential tails, Erd\H{o}s-R\'enyi $d$-regular graphs any polynomial sparsity parameter, non-mean-field such as band bandwidth. The proof builds on recent tools, including theory Matrix Dyson Equation developed in [Ajanki, Erd\H{o}s, Kr\"uger 2019]. use these asymptotics an important input complexity landscapes our companion papers [Ben Arous, Bourgade, McKenna 2021; 2021].