Abstract: Approximation of convex bodies by random polytopes is one of the oldest topics of geometric probability. Its origins go back to the fam ous four-point problem of Sylvester in the 1860s. The most frequently inves tigated model of random polytopes is when one takes the convex hull of n i. i.d. uniform random points in a d-dimensional convex body K. Certain geomet ric quantities of the random polytopes, such as volume, surface area, etc, approach those of K with high probability as n tends to infinity. It is one of the important questions how fast this convergence is and how it depends on the facial structure of K.

In this talk we will consider a var iant of the uniform model in which we generate the random objects (called r andom ball-polytopes) by the intersection of equal radius closed balls inst ead of closed half-spaces. We will primarily investigate the asymptotic beh aviour of the number of facets of random ball-polytopes in smooth convex bo dies as n tends to infinity. We will generalize some earlier joint results with P. Kevei and V. Vigh from the plane to arbitrary dimensions. We will p rove the interesting phenomenon that the expected number of proper facets o f uniform random ball-polytopes in a ball tends to a constant that depends only on the dimension. DTSTAMP:20230209T050937Z DTSTART;TZID=Europe/Budapest:20180321T140000 DTEND;TZID=Europe/Budapest:20180321T160000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR