Zhou Fan

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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 $R^{n}$ interacting through a symmetric matrix $X \in R^{n \times n}$ . When eigenvectors of $X$ are Haar-uniform on the orth…

math.PR2026

Kronecker-product random matrices and a matrix least squares problem

Zhou Fan, Renyuan Ma

We study the eigenvalue distribution and resolvent of a Kronecker-product random matrix model $A \otimes I_{n \times n}+I_{n \times n} \otimes B+Î\otimes Î\in \mathbb{C}^{n^2 \ti…

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…