Localization in Gaussian disordered systems at low temperature
Probability
2021-08-30 v4 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1906.05502,
title = {Localization in Gaussian disordered systems at low temperature},
author = {Erik Bates and Sourav Chatterjee},
journal= {arXiv preprint arXiv:1906.05502},
year = {2021}
}
Comments
67 pages. Minor edits in this revision