COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Isoperimetric and concentration inequalities - equivalence and applications

## Isoperimetric and concentration inequalities - equivalence and applicationsAdd to your list(s) Download to your calendar using vCal - Milman, E (Technion)
- Tuesday 07 June 2011, 14:00-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Discrete Analysis Given a metric space equipped with a measure, various ways exist for studying the interaction between measure and metric. A very strong form is given by isoperimetric inequalities, which for a set of given measure, provide a lower bound on its boundary measure. A much weaker form is given by concentration inequalities, which quantify large-deviation behavior of measures of separated sets. There are also other tiers, interpolating between these two extremes, such as the tier of Sobolev-type inequalities. It is classical (by results of Cheeger, Maz’ya, Gromov—Milman andothers) that isoperimetric inequalities imply corresponding functional versions, which in turn imply concentration counterparts. However, in general, these implications cannot be reversed. We show that under a suitable (possibly negative) lower bound on the generalized Ricci curvature of a Riemannian-manifold-with-density, completely general concentration inequalities imply back their isoperimetric counterparts, up to dimension mph{independent} bounds. Consequently, in such spaces, all of the above tiers of the hierarchy are equivalent, clarifying the role which curvature plays in the interaction between measure and metric. Several applications of this equivalence will be presented, ranging from Statistical Mechanics to Spectral Geometry. Time permitting, we will also present new mph{sharp} isoperimetric inequalities, generalizing classical results due to P. L’evy, Sudakov—Tsirelson and Borell, Gromov and Bakry—Ledoux, into one single form.
This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsLand Economy Departmental Seminar Series World Oral Literature Project Surfaces, Microstructure and Fracture Group## Other talksDrugs and Alcohol Cafe Synthetique: Synthetic Biology Industry Night TBA Immigration policy-making beyond 'Western liberal democracies' Positive definite kernels for deterministic and stochastic approximations of (invariant) functions |