2023/11/16 by Hongbin Chen, Chen, Hong-Bin
Economics, Econometrics and Finance · Materials Science · Physics and Astronomy · #82B44 #82D30 #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Material Dynamics and Properties #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2311.09880
openalex publication_date 2023/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: 1) the averaged self-overlap converges; 2) the self-overlap concentrates; 3) the infimum optimizes over paths whose right endpoints are the limit of self-overlap. Lastly, using these, we directly verify the equivalence between the variational formula obtained in [arXiv:2303.16284] and Panchenko's generalized Parisi formula in [Ann. Probab., 46(2):865-896].