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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Discrete Ricci curvature with applications

## Discrete Ricci curvature with applicationsAdd to your list(s) Download to your calendar using vCal - Ollivier, Y (Universite Paris-Sud)
- Wednesday 18 May 2011, 14:00-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Discrete Analysis We define a notion of discrete Ricci curvature for a metric measure space by looking at whether “small balls are closer than their centers are”. In a Riemannian manifolds this gives back usual Ricci curvature up to scaling. This definition is very easy to apply in a series of examples such as graphs (eg the discrete cube has positive curvature). We are able to generalize several Riemannian theorems in positive curvature, such as concentration of measure and the log-Sobolev inequality. This definition also allows to prove new theorems both in the Riemannian and discrete case: for example improved bounds on spectral gap of the Laplace-Beltrami operator, and fast convergence results for some Monte Carlo Markov Chain methods. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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