We prove a concentration inequality for the np norm on the npsphere for p, q > 0. This inequality, which generalizes results of Schechtman and Zinn (2000), is used to study the distance between the cone measure and surface measure on the sphere of n p. In particular, we obtain a significant strengthening of the inequality derived by Naor and Romik (2003), and calculate the precise dependence of the constants that appeared there on p.
|Original language||English (US)|
|Number of pages||35|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Mar 2007|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Concentration inequalities
- Cone measure
- Convex geometry.
- Geometry of
- Surface measure