Open Access
November 2020 Localization in Gaussian disordered systems at low temperature
Erik Bates, Sourav Chatterjee
Ann. Probab. 48(6): 2755-2806 (November 2020). DOI: 10.1214/20-AOP1436


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.


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Erik Bates. Sourav Chatterjee. "Localization in Gaussian disordered systems at low temperature." Ann. Probab. 48 (6) 2755 - 2806, November 2020.


Received: 1 August 2019; Revised: 1 February 2020; Published: November 2020
First available in Project Euclid: 20 October 2020

MathSciNet: MR4164453
Digital Object Identifier: 10.1214/20-AOP1436

Primary: 60K37
Secondary: 60G15 , 60G17 , 82B44 , 82D30 , 82D60

Keywords: Directed polymers , Gaussian disorder , path localization , Replica overlap , Spin glasses

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 6 • November 2020
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