Ferenc Fodor 

Title: Asymptotic expansions for generalized random polygons

Abstract: There has been quite a lot of work done recently in various
generalized models of random polytopes in convex bodies. One such model
is when one takes n independent identically distributed uniform random
points from a suitable convex body and considers the intersection of all
congruent closed balls that contain the points. The resulting
intersection is called a random ball-polytope (disc-polygon in the plane).
In this talk we discuss the behaviour of the vertex number of random
disc-polygons.
We prove series expansions for the expectation of the
vertex number and area of random disc-polygons depending on the degree
of smoothness of the boundary of the convex disc.
Joint work with N. Montenegro (University of Szeged, Hungary).