40 citations · 90 across the 18 of their papers we have counts for
18 papers
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…
Liouville theorem for -harmonic maps under non-negative -Ricci curvature for non-positive
Kazuhiro Kuwae, Songzi Li, Xiangdong Li +1
Let be a -vector field on an -dimensional complete Riemannian manifold . We prove a Liouville theorem for -harmonic maps satisfying various growth conditions…
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…
On the Renyi entropy power and the Gagliardo-Nirenberg-Sobolev inequality on Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this paper, we prove the concavity of the Renyi entropy power for nonlinear diffusion equation (NLDE) associated with the Laplacian and the Witten Laplacian on compact Riemannia…
K-groups: A Generalization of K-means Clustering
Songzi Li, Maria L. Rizzo
We propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns obse…
-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this survey paper, we give an overview of our recent works on the study of the -entropy for the heat equation associated with the Witten Laplacian on super-Ricci flows and th…
Hamilton differential Harnack inequality and -entropy for Witten Laplacian on Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the $…
On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows
Songzi Li, Xiang-Dong Li
In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation associated with the time depe…
-entropy, super Perelman Ricci flows and -Ricci solitons
Songzi Li, Xiang-Dong Li
In this paper, we prove the characterization of the -super Perelman Ricci flows by various functional inequalities and gradient estimate for the heat semigroup generat…
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…
Harnack inequalities and -entropy formula for Witten Laplacian on Riemannian manifolds with -super Perelman Ricci flow
Songzi Li, Xiang-Dong Li
In this paper, we prove logarithmic Sobolev inequalities and derive the Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on complete Riemannian manifolds…
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…
-entropy formula for the Witten Laplacian on manifolds with time dependent metrics and potentials
Songzi Li, Xiang-Dong Li
In this paper, we develop a new approach to prove the -entropy formula for the Witten Laplacian via warped product on Riemannian manifolds and give a natural geometric interpret…