Publication date
January 2007
DOIAbstract
We answer an old question: what are possible growth rates of the expected number of vector-maximal points in a uniform sample from a polytope
We answer an old question: what are possible growth rates of the expected number of vector-maximal points in a uniform sample from a polytope
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
AbstractEvery coherent probability (= F-probability) F on a finite sample space Ωk with k elements d...
The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a ...
A maximal vector of a set is one which is not less than any other vector in all components. We deriv...
The Maximal points in a set S are those that are not dominated by any other point in S. Such points ...
International audienceWe consider random polytopes defined as the convex hull of a Poisson point pro...
Let C be a planar region. Choose n points p1,⋯,pnI.I.D. from the uniform distribution over C. Let MC...
Assume K ⊂ Rd is a convex body and X is a (large) finite subset of K. How many convex polytopes are ...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
AbstractWe describe a maximum entropy approach for computing volumes and counting integer points in ...
In an evolutionary system in which the rules of mutation are local in nature, the number of possible...
International audienceLet K be a compact convex body in $Rd$, let $Kn$ be the convex hull of n point...
Assume that Y is a noisy version of a point set X in convex position. How many vertices does the con...
The main result of the Thesis is a lower bound for the maximal possible number of facets of a 0/1 po...
The definition of random polytope adopted in this paper restricts consideration to those probability...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
AbstractEvery coherent probability (= F-probability) F on a finite sample space Ωk with k elements d...
The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a ...
A maximal vector of a set is one which is not less than any other vector in all components. We deriv...
The Maximal points in a set S are those that are not dominated by any other point in S. Such points ...
International audienceWe consider random polytopes defined as the convex hull of a Poisson point pro...
Let C be a planar region. Choose n points p1,⋯,pnI.I.D. from the uniform distribution over C. Let MC...
Assume K ⊂ Rd is a convex body and X is a (large) finite subset of K. How many convex polytopes are ...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
AbstractWe describe a maximum entropy approach for computing volumes and counting integer points in ...
In an evolutionary system in which the rules of mutation are local in nature, the number of possible...
International audienceLet K be a compact convex body in $Rd$, let $Kn$ be the convex hull of n point...
Assume that Y is a noisy version of a point set X in convex position. How many vertices does the con...
The main result of the Thesis is a lower bound for the maximal possible number of facets of a 0/1 po...
The definition of random polytope adopted in this paper restricts consideration to those probability...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
AbstractEvery coherent probability (= F-probability) F on a finite sample space Ωk with k elements d...
The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a ...
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