Jimenez, Hugo and Naszódi, Márton and Villa, Rafael (2014) Push forward measures and concentration phenomena. Mathematische Nachrichten, 287 (5-6). pp. 585-594. ISSN 0025-584X
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Abstract
In this note we study how a concentration phenomenon can be transferred from one measure μ to a push-forward measure ν. In the first part, we push forward μ by a central projection, and obtain a concentration inequality in terms of the medians of the given norms (with respect to μ) and the Banach-Mazur distance between them. This approach is finer than simply bounding the concentration of the push forward measure in terms of the Banach-Mazur distance between K and L. As a consequence we show that any normed probability space with exponential type concentration is far (even in an average sense) from subspaces of l_p. The sharpness of this result is shown by considering the inline image spaces.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria |
| Depositing User: | Dr. Márton Naszódi |
| Date Deposited: | 24 Sep 2014 12:00 |
| Last Modified: | 01 Sep 2015 23:15 |
| URI: | http://real.mtak.hu/id/eprint/16399 |
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