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Cugliandolo-Kurchan equations for dynamics of Spin-Glasses

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arxiv math/0409273 v1 pith:4D5CNW3A submitted 2004-09-16 math.PR cond-mat.stat-mechmath-phmath.MP

Gerard Ben Arous , Amir Dembo , Alice Guionnet This is my paper · ORCID
classification math.PRcond-mat.stat-mechmath-phmath.MP
keywords dynamicsequationsalmostapproachingconvergecorrelationcugliandolocugliandolo-kurchan
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abstract

We study the Langevin dynamics for the family of spherical $p$-spin disordered mean-field models and prove that in the limit of system size $N$ approaching infinity, the empirical state correlation and integrated response functions converge almost surely and uniformly in time, to the non-random unique strong solution of a pair of explicit non-linear integro-differential equations introduced by Cugliandolo and Kurchan.

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  1. Adaptive kernel predictors from feature-learning infinite limits of neural networks

    cs.LG 2025-02 conditional novelty 7.0 of 10

    Feature-learning infinite-width neural networks are kernel machines with data-dependent kernels, defined by a min-max saddle point (Bayesian/Langevin) or a DMFT fixed point (gradient flow with weight decay).

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