The Levy concentration phenomenon for special functions on rank-one symmetric spaces (Q5937115)

The main topic of this paper is to study in some detail the measure concentration phenomenon for compact, rank-one symmetric spaces. Paul Levy discovered the surprising phenomenon of measure concentration of Lipschitz maps for certain sequences of spaces as the dimension goes to infinity. Further, it has been explored in a geometrical framework by M. Gromov and V. Milman. In particular, the authors investigate the role of zonal eigenfunctions of the Laplacian and show that the push-forward measures of a wide class of observables associated with these functions exhibit a much stronger concentration than the estimate one gets from the isoperimetric inequality of Gromov and Levy.