Universality of random kernel matrix spectra for isotropic log-concave distributions

Let $X_i$ be iid random vectors from a normalized isotropic log-concave distribution. Universality conjecture. The results of Theorem~ hold for these random vectors. This conjectures that the universality results for random kernel matrices established under the paper's preceding hypotheses extend to the isotropic log-concave setting; the source does not provide a resolution.