3 papers
math.PR2026
The invariance principle for inhomogeneous Diophantine approximations
Songzi Li
We establish the central limit theorem and the invariance principle for the inhomogeneous Diophantine approximations. The proof employs the cumulant method, which was developed by…
math.PR2025
The periodic Lorentz gas in the Boltzmann-Grad limit: the free path length and the K-S entropy
Songzi Li
We study the periodic Lorentz gas in the Boltzmann-Grad limit, whose convergence was rigorously established in the seminal work of Marklof-Strömbergsson. Extending the two dimensi…
math.PR2024
Langevin deformation for Rényi entropy on Wasserstein space over Riemannian manifolds
Rong Lei, Songzi Li, Xiang-Dong Li
We introduce the Langevin deformation for the Rényi entropy on the -Wasserstein space over or a Riemannian manifold, which interpolates between the porous medi…