Push forward measures and concentration phenomena

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


Download (315kB) | Preview


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
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

Actions (login required)

Edit Item Edit Item