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On the Law of Large Numbers for the Empirical Measure Process of Generalized Dyson Brownian Motion 期刊论文
JOURNAL OF STATISTICAL PHYSICS, 2020, 页码: 29
作者:  Li, Songzi;  Li, Xiang-Dong;  Xie, Yong-Xiao
收藏  |  浏览/下载:151/0  |  提交时间:2021/01/14
Generalized Dyson Brownian motion  McKean-Vlasov equation  Gradient flow  Optimal transportation  Voiculescu free entropy  Law of Large Numbers  Propagation of chaos  
W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons 期刊论文
JOURNAL OF GEOMETRIC ANALYSIS, 2020, 卷号: 30, 期号: 3, 页码: 3149-3180
作者:  Li, Songzi;  Li, Xiang-Dong
收藏  |  浏览/下载:147/0  |  提交时间:2020/09/23
W-entropy  Witten Laplacian  CD(K, m)-condition  (K, m)-Ricci solitons  (K, m)-super Perelman Ricci flows  (K, m)-Perelman Ricci flow  Gaussian solitons  
Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces 期刊论文
MANUSCRIPTA MATHEMATICA, 2020, 页码: 31
作者:  Kuwada, Kazumasa;  Li, Xiang-Dong
收藏  |  浏览/下载:165/0  |  提交时间:2020/05/24
W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds 期刊论文
SCIENCE CHINA-MATHEMATICS, 2018, 卷号: 61, 期号: 8, 页码: 1385-1406
作者:  Li, Songzi;  Li, Xiang-Dong
收藏  |  浏览/下载:171/0  |  提交时间:2018/09/08
W-entropy  Witten Laplacian  Langevin deformation  (K, m)-super Ricci flows  
Hamilton differential Harnack inequality and W-entropy for Witten Laplacian on Riemannian manifolds 期刊论文
JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 卷号: 274, 期号: 11, 页码: 3263-3290
作者:  Li, Songzi;  Li, Xiang-Dong
收藏  |  浏览/下载:167/0  |  提交时间:2018/07/30
Hamilton differential Harnack inequality  W-entropy  Super Ricci flows  
wentropyformulasonsuperricciflowsandlangevindeformationonwassersteinspaceoverriemannianmanifolds 期刊论文
sciencechinamathematics, 2018, 卷号: 61, 期号: 8, 页码: 1385
作者:  Li Songzi;  Li Xiangdong
收藏  |  浏览/下载:186/0  |  提交时间:2020/01/10
Hamilton's Harnack inequality and the W-entropy formula on complete Riemannian manifolds 期刊论文
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 卷号: 126, 期号: 4, 页码: 1264-1283
作者:  Li, Xiang-Dong
收藏  |  浏览/下载:142/0  |  提交时间:2018/07/30
Hamilton's Harnack inequality  Gradient estimates  Logarithmic heat kernel  Witten Laplacian  W-entropy formula  
THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS 期刊论文
PACIFIC JOURNAL OF MATHEMATICS, 2015, 卷号: 278, 期号: 1, 页码: 173-199
作者:  Li, Songzi;  Li, Xiang-Dong
收藏  |  浏览/下载:138/0  |  提交时间:2018/07/30
Perelman's W-entropy for the Fokker-Planck equation over complete Riemannian manifolds 期刊论文
BULLETIN DES SCIENCES MATHEMATIQUES, 2011, 卷号: 135, 期号: 6-7, 页码: 871-882
作者:  Li, Xiang-Dong
收藏  |  浏览/下载:105/0  |  提交时间:2018/07/30