English

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

R2 v1 2026-06-23T09:52:21.243Z