| dc.contributor.author |
Gatzouras, D |
en |
| dc.contributor.author |
Giannopoulos, A |
en |
| dc.date.accessioned |
2014-06-06T06:49:37Z |
|
| dc.date.available |
2014-06-06T06:49:37Z |
|
| dc.date.issued |
2009 |
en |
| dc.identifier.issn |
00212172 |
en |
| dc.identifier.uri |
http://dx.doi.org/10.1007/s11856-009-0007-z |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/4685 |
|
| dc.title |
Threshold for the volume spanned by random points with independent coordinates |
en |
| heal.type |
journalArticle |
en |
| heal.identifier.primary |
10.1007/s11856-009-0007-z |
en |
| heal.publicationDate |
2009 |
en |
| heal.abstract |
Let μ be an even compactly supported Borel probability measure on the real line. For every N > n consider N independent random vectors X 1, ..., X N in ℝ n , with independent coordinates having distribution μ. We establish a sharp threshold for the volume of the random polytope K N :=conv{X 1, ..., X N }, provided that the Legendre transform λ of the cumulant generating function of μ satisfies the condition x ↑ α - ln μ ([x,∞ )/λ (x)= 1 , where α is the right endpoint of the support of μ. The method and the result generalize work of Dyer, Füredi and McDiarmid on 0/1 polytopes. We verify (*) for a large class of distributions. © 2008 Hebrew University Magnes Press. |
en |
| heal.journalName |
Israel Journal of Mathematics |
en |
| dc.identifier.issue |
1 |
en |
| dc.identifier.volume |
169 |
en |
| dc.identifier.doi |
10.1007/s11856-009-0007-z |
en |
| dc.identifier.spage |
125 |
en |
| dc.identifier.epage |
153 |
en |