The Riemannian Langevin equation and conic programs
Every regular convex cone $K \subset \mathbb{R}^{n+1}$ has a canonical barrier $F$ and a canonical Hessian metric $g=D^2F$. We study the Riemannian Langevin equation on $(K,g)$, establishing several relations between Brownian motion on $(K,g)$ and $F$. Explicit formulas are presented for some fundamental cones, including the Lorentz cone.
Authors
- M. Govind
- Yu Tianmin
Publication Details
- Journal
- Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES
- Published
- 2025-09-01
- DOI
- https://doi.org/10.21915/bimas.2025302
- Primary Topic
- Statistical Mechanics and Entropy
- Type
- article
- Field-Weighted Citation Impact
- 0.00