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arXiv · 1906.05502

Localization in Gaussian disordered systems at low temperature

Erik Bates·Sourav Chatterjee
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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.

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Erik Bates, Sourav Chatterjee. 2019-06-13. Localization in Gaussian disordered systems at low temperature. https://arxiv.org/abs/1906.05502

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