2026-09-23T11:45:36Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/121292 2023-12-13 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Dey, Partha Sarathi Song , Renming Song , Renming Baryshnikov, Yuliy Liu, Jingbo Nguyen, Oanh 2023-08 application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-08-01 The student, Qiang Wu, accepted the attached license on 2023-07-05 at 16:56. The student, Qiang Wu, submitted this Dissertation for approval on 2023-07-05 at 17:06. This Dissertation was approved for publication on 2023-07-13 at 15:55. DSpace SAF Submission Ingestion Package generated from Vireo submission #19265 on 2023-12-04 at 17:17:43 Cluster expansion approach and fluctuation results in mean field spin glass theory Wu, Qiang 2023-07-13 Free Energy Spin Glass Cluster Expansion 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. Text eng https://hdl.handle.net/2142/121292 Copyright 2023 Qiang Wu Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics