Tématerületi Kiválósági Program 2021(TKP2021-NVA-09) Támogató: NKFIH
OTKA K 134814(OTKA K 134814) Támogató: NKFIH
We consider a probability model in which the hull of a sample of i.i.d. uniform random
points from a convex disc K is formed by the intersection of all translates of another
suitable fixed convex disc L that contain the sample. Such an object is called a random
L -polygon in K . We assume that both K and L have C^2_+ C + 2 smooth boundaries,
and we prove upper bounds on the variance of the number of vertices and missed area
of random L -polygons assuming different curvature conditions. We also transfer some
of our result to a circumscribed variant of this model.