Cluster expansion approach and fluctuation results in mean field spin glass theory
Wu, Qiang
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https://hdl.handle.net/2142/121292
Description
Title
Cluster expansion approach and fluctuation results in mean field spin glass theory
Author(s)
Wu, Qiang
Issue Date
2023-07-13
Director of Research (if dissertation) or Advisor (if thesis)
Dey, Partha Sarathi
Song , Renming
Doctoral Committee Chair(s)
Song , Renming
Committee Member(s)
Baryshnikov, Yuliy
Liu, Jingbo
Nguyen, Oanh
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Free energy, spin glass, cluster expansion
Abstract
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.
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