On the mean width of log-concave functions
arXiv:1210.4325 · doi:10.1007/978-3-642-29849-3_22
Abstract
In this work we present a new, natural, definition for the mean width of log-concave functions. We show that the new definition coincide with a previous one by B. Klartag and V. Milman, and deduce some properties of the mean width, including an Urysohn type inequality. Finally, we prove a functional version of the finite volume ratio estimate and the low-M* estimate.
15 pages