For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain: (i) a version of “complete” path localization for directed polymers that is not available even for exactly solvable models, and (ii) a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda–Guerra identities.
"Localization in Gaussian disordered systems at low temperature." Ann. Probab. 48 (6) 2755 - 2806, November 2020. https://doi.org/10.1214/20-AOP1436