Cluster expansion approach and fluctuation results in mean field spin glass theory

Mean field spin glass theory has undergone tremendous development in the last twenty years, particularly with the proof of the Parisi formula for evaluating limiting free energy at any temperature. However, as a variational formula, it is less effective for dealing with higher-order asymptotics, such as related fluctuation problems. This thesis, composed of several papers, is devoted to establishing fluctuation results for a broad range of mean field spin glass models by developing several different techniques.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Wu, Qiang

Contributors dc:contributor

• Dey, Partha Sarathi
• Song , Renming
• Baryshnikov, Yuliy
• Liu, Jingbo
• Nguyen, Oanh

• Free Energy
• Spin Glass
• Cluster Expansion

Statement dc:rights

• Copyright 2023 Qiang Wu

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121292

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121292