# Localization in Gaussian disordered systems at low temperature

## TL;DR

This paper demonstrates that in Gaussian disordered systems at low temperatures, the Gibbs measure concentrates around a few states, providing new insights into localization phenomena in spin glasses and directed polymers.

## Contribution

It introduces a unified argument showing localization in Gaussian disordered systems, enabling results on path localization and Gibbs state exhaustiveness without relying on traditional identities.

## Key findings

- Gibbs measure localizes in small neighborhoods of few states
- Path localization for directed polymers achieved without exact solvability
- Gibbs states are exhaustive in spin glasses without Ghirlanda-Guerra identities

## 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.