Random points, convex bodies, lattices

Details Random points, convex bodies, lattices Random points, convex bodies, lattices

2003-04-28

arxiv.org/abs/math/0304462v1

Proceedings of the ICM, Beijing 2002, vol. 3, 527--536

Mathematics

Combinatorics

Scientific paper

Assume $K$ is a convex body in $R^d$, and $X$ is a (large) finite subset of $K$. How many convex polytopes are there whose vertices come from $X$? What is the typical shape of such a polytope? How well the largest such polytope (which is actually $\conv X$) approximates $K$? We are interested in these questions mainly in two cases. The first is when $X$ is a random sample of $n$ uniform, independent points from $K$ and is motivated by Sylvester's four-point problem, and by the theory of random polytopes. The second case is when $X=K \cap Z^d$ where $Z^d$ is the lattice of integer points in $R^d$. Motivation comes from integer programming and geometry of numbers. The two cases behave quite similarly.

Affiliated with

Also associated with

No associations

Rating

Random points, convex bodies, lattices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random points, convex bodies, lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random points, convex bodies, lattices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-333998