Localization and free energy asymptotics in disordered statistical mechanics and random growth models

Abstract

This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin glasses and directed polymers, wherein the ensembles exhibit localization which is physically phenomenological. We quantify this behavior in several ways and establish connections to properties of the limiting free energy. We also consider two popular zero-temperature polymer models, namely first- and last-passage percolation. For these random growth models, we investigate the order of fluctuations in their growth rates, which are analogous to free energy.

(v6. corrected typos) Ph.D. thesis (Stanford University, 2019), xii+295 pages; Chapter 2 gives a unified presentation of arXiv:1612.03443 and arXiv:1708.03713, Chapter 3 includes content of arXiv:1906.05502, Chapter 4 includes content of arXiv:1810.03215, Chapter 5 includes content of arXiv:1810.03656, MATLAB code in appendix

References in corpus (11)

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• Proof of the path localization conjecture for directed polymers