40 citations · 90 across the 18 of their papers we have counts for
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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…
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 mediu…
Asymptotics of the free path length in the periodic Lorentz gas in the Boltzmann-Grad limit
Songzi Li
We study the distribution of the free path length in the periodic Lorentz gas in the Boltzmann-Grad limit. For any unimodular Euclidean lattice and any smooth initial velocity dist…
The convergence rates for the superdiffusion in the Boltzmann-Grad limit of the periodic Lorentz gas
Songzi Li
In this article, we obtain the rates of convergence for superdiffusion in the Boltzmann-Grad limit of the periodic Lorentz gas, which is one of the fundamental models to study diff…
Matrix Dirichlet processes
Songzi Li
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators…
-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds
Songzi Li, Xiang-Dong Li
We introduce Perelman's -entropy and prove the -entropy formula along the geodesic flow on the -Wasserstein space over compact Riemannian manifolds equipped with Otto's…
Dyson processes on the octonion algebra
Songzi Li
We consider Brownian motion on symmetric matrices of octonions, and study the law of the spectrum. Due to the fact that the octonion algebra is nonassociative, the dimension of the…
On the Law of Large Numbers for the empirical measure process of Generalized Dyson Brownian motion
Songzi Li, Xiang-Dong Li, Yong-Xiao Xie
We study the generalized Dyson Brownian motion (GDBM) of an interacting -particle system with logarithmic Coulomb interaction and general potential . Under reasonable conditi…
Generalized Dyson Brownian motion, McKean-Vlasov equation and eigenvalues of random matrices
Songzi Li, Xiang-Dong Li, Yong-Xiao Xie
Using Itô's calculus and the mass optimal transportation theory, we study the generalized Dyson Brownian motion (GDBM) and the associated McKean-Vlasov evolution equation with an e…