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math.PR2023★ 2 cited
High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
Krishnakumar Balasubramanian, Promit Ghosal, Ye He
We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating…
math.PR2023
Fractal geometry of the PAM in 2D and 3D with white noise potential
Promit Ghosal, Jaeyun Yi
We study the parabolic Anderson model (PAM) \begin{equation} {\partial \over \partial t}u(t,x) =\frac{1}{2}Δu(t,x) + u(t,x)ξ(x), \quad t>0, x\in \mathbb{R}^d, \quad \text{and} \qua…