W-entropy and Langevin deformation on Wasserstein space over Riemannian manifolds
发布时间：2018-03-20 点击次数：
| 报告题目： |
W-entropy and Langevin deformation on Wasserstein space over Riemannian manifolds |
| 报 告 人： |
李向东 研究员(中国科学院应用数学所) |
| 报告时间： |
2018年03月22日 10:30--11:30 |
| 报告地点： |
理学院东北楼二楼报告厅（209） |
| 报告摘要： |
Inspired by G. Perelman’s seminal work on the entropy formula for the Ricci flow, we prove the W-entropy formula for the heat equation associated with the Witten Laplacian on n-dimensional complete Riemannian manifolds with the CD(K, m) condition, where K ∈ R and m ∈ [n, ∞]. Moreover, we prove an analogue of the W-entropy formula for the geodesic flow on the Wasserstein space over Riemannian manifolds. Our result improves an earlier result due to J. Lott and C. Villani on the geodesic displacement convexity of the Boltzmann-Shannon entropy on Riemannian manifolds with non-negative Ricci curvature. To better understand the similarity between above two W-entropy formulas, we introduce the Langevin deformation of geometric flows on the tangent bundle over the Wasserstein space and prove an extension of the W-entropy formula for the Langevin deformation. Finally, we study the hydrodynamic limit of the Langevin deformation.
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