DiscoverDiscrete AnalysisDiscrete Ricci curvature with applications
Discrete Ricci curvature with applications

Discrete Ricci curvature with applications

Update: 2011-06-03
Share

Description

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.
Comments 
Top Podcasts
The Best New Comedy Podcast Right Now – June 2024The Best News Podcast Right Now – June 2024The Best New Business Podcast Right Now – June 2024The Best New Sports Podcast Right Now – June 2024The Best New True Crime Podcast Right Now – June 2024The Best New Joe Rogan Experience Podcast Right Now – June 20The Best New Dan Bongino Show Podcast Right Now – June 20The Best New Mark Levin Podcast – June 2024
In Channel
Positive projections

Positive projections

2011-07-0759:13

The logarithmic Laplace transform in convex geometry

The logarithmic Laplace transform in convex geometry

2011-06-2456:59

Gradient flows of the entropy for finite Markov chains

Gradient flows of the entropy for finite Markov chains

2011-06-2459:26

Applications of Discrete Harmonic Analysis, Probabilistic Method and Linear Algebra in Fixed-Parameter Tractability and Kernelization

Applications of Discrete Harmonic Analysis, Probabilistic Method and Linear Algebra in Fixed-Parameter Tractability and Kernelization

2011-06-2454:57

Quantitative geometry and efficient classification procedures

Quantitative geometry and efficient classification procedures

2011-06-2251:42

Towards an entropy-based sumset calculus for additive combinatorics and convex geometry

Towards an entropy-based sumset calculus for additive combinatorics and convex geometry

2011-06-2058:28

Is asymptotic extremal graph theory of dense graphs trivial?

Is asymptotic extremal graph theory of dense graphs trivial?

2011-06-2001:02:20

Stochastic completeness for random walks and jump processes

Stochastic completeness for random walks and jump processes

2011-06-2001:02:47

Isoperimetric and concentration inequalities

Isoperimetric and concentration inequalities

2011-06-1301:07:42

Singular integrals in bad neighborhoods II: Stochastic Optimal Control and sharp estimates of Singular Integrals

Singular integrals in bad neighborhoods II: Stochastic Optimal Control and sharp estimates of Singular Integrals

2011-06-1301:07:02

Computability and Complexity of Julia Sets

Computability and Complexity of Julia Sets

2011-06-0354:15

Ricci curvature of Finsler manifolds, towards applications in the geometry of Banach spaces

Ricci curvature of Finsler manifolds, towards applications in the geometry of Banach spaces

2011-06-0358:54

Singular integrals in bad neighborhoods I: Singular integrals for Geometric Measure Theory

Singular integrals in bad neighborhoods I: Singular integrals for Geometric Measure Theory

2011-06-0359:17

Vertex Sparsifiers and Lipschitz Extendability

Vertex Sparsifiers and Lipschitz Extendability

2011-06-0354:09

Favourite distances in high dimensions

Favourite distances in high dimensions

2011-06-0352:11

How to Play Unique Games Against a Semi-Random Adversary

How to Play Unique Games Against a Semi-Random Adversary

2011-06-0354:32

Discrete Ricci curvature with applications

Discrete Ricci curvature with applications

2011-06-0301:12:23

3-terms arithmetic progressions in finite fields (IV)

3-terms arithmetic progressions in finite fields (IV)

2011-06-0301:03:45

Rates of convergence in the entropic central limit theorem

Rates of convergence in the entropic central limit theorem

2011-06-0350:24

3-terms arithmetic progressions in finite fields (III)

3-terms arithmetic progressions in finite fields (III)

2011-06-0301:01:03

loading
Google Play
Download from Google Play
Castbox
Download from App Store
usUnited States
00:00
00:00
x

0.5x

0.8x

1.0x

1.25x

1.5x

2.0x

3.0x

Sleep Timer

Off

End of Episode

5 Minutes

10 Minutes

15 Minutes

30 Minutes

45 Minutes

60 Minutes

120 Minutes

Discrete Ricci curvature with applications

Discrete Ricci curvature with applications

Steve Greenham