Limit theorems for random polytopes with vertices on convex surfaces

Variance estimates for random disc-polygons in smooth convex discs

“…Obtaining information on the second order properties of random variables associated with random polytopes is much harder than on first order properties. It is only recently that variance estimates, laws of large numbers, and central limit theorems have been proved in various models, see, for example, Bárány, Fodor, Vígh [2], Bárány, Reitzner [5], Bárány, Vu [6], Fodor, Hug, Ziebarth [13], Böröczky, Fodor, Reitzner, Vígh [9], Reitzner [18,19], Schreiber, Yukich [26], Vu [27,31], and the very recent papers by Thäle, Turchi, Wespi [28], Turchi, Wespi [29]. For an overview, we refer to Bárány [1] and Schneider [24].…”