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math.PR2026
Mixing times of Langevin dynamics for spiked matrix models
Reza Gheissari, Curtis Grant, Tianmin Yu
We investigate the Langevin dynamics for Wigner matrices with a spherical spike, in the regime where the signal-to-noise ratio is large, but order one. For large, order-, si…
math.PR2023
Siegel Brownian motion
Govind Menon, Tianmin Yu
We construct an analogue of Dyson Brownian motion in the Siegel half-space H that we term Siegel Brownian motion. Given βin (0,\infty], a stochastic flow for Z_t in H is introduced…
math.PR2023
The Riemannian Langevin equation and conic programs
Govind Menon, Tianmin Yu
Diffusion limits provide a framework for the asymptotic analysis of stochastic gradient descent (SGD) schemes used in machine learning. We consider an alternative framework, the Ri…