Random points, convex bodies, lattices
| dc.creator | Bárány, Imre | |
| dc.date | 2003-04-28 | |
| dc.date.accessioned | 2026-07-07T04:57:32Z | |
| dc.date.available | 2026-07-07T04:57:32Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0304462 | |
| dc.identifier | http://arxiv.org/abs/math/0304462 | |
| dc.identifier | Proceedings of the ICM, Beijing 2002, vol. 3, 527--536 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67294 | |
| dc.subject | Combinatorics | |
| dc.subject | 52A22, 05A16, 52C07 | |
| dc.title | Random points, convex bodies, lattices | |
| dc.type | text |