3 papers
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.NA2023
Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank
Tianmin Yu, Shixin Zheng, Jianfeng Lu +2
This paper introduces two explicit schemes to sample matrices from Gibbs distributions on , the manifold of real positive semi-definite (PSD) matrices of size $…
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…