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math.PR2026
Dynamical mean-field limit and replica-symmetric free energy for the orthogonally-invariant SK model
Zhou Fan, Theodor Misiakiewicz, Leda Wang +1
We study a class of diffusion processes on interacting through a symmetric matrix . When eigenvectors of are Haar-uniform on the orth…
math.PR2026
Anisotropic local law for non-separable sample covariance matrices
Zhou Fan, Renyuan Ma, Elliot Paquette +1
We establish local laws for sample covariance matrices $K = N^{-1}\sum_{i=1}^N \g_i\g_i^*$ where the random vectors $\g_1, \ldots, \g_N \in \R^n$ are independent with common covari…
stat.ML2026
High-dimensional learning dynamics of multi-pass Stochastic Gradient Descent in multi-index models
Zhou Fan, Leda Wang
The learning dynamics of Stochastic Gradient Descent (SGD) are believed to play an important role in influencing the generalization properties of trained models. While the precise…