9 citations · 18 across the 6 of their papers we have counts for
6 papers
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…
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…