Abstract
We survey some recent rigorous results regarding the dynamics of spin glasses. We first survey recent results with Gheissari and Ben Arous regarding spectral gaps for these models. In particular, we briefly present the extension of the large deviations based approach of Ben Arous and Jagannath [Commun. Math. Phys. 361, 1–52 (2018)] to the setting of spherical spin glasses, unifying the treatment of the Ising and spherical models. We then turn to the new bounding flows method introduced by Ben Arous et al. [“Bounding flows for spherical spin glass dynamics,” e-print arXiv:1808.00929] regarding the nonactivated dynamics. We end with a report on progress on activated dynamics.
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