Volume réticulaire critique d'un simplexe.
Volume thresholds for Gaussian and spherical random polytopes and their duals
Let g be a Gaussian random vector in ℝⁿ. Let N = N(n) be a positive integer and let be the convex hull of N independent copies of g. Fix R > 0 and consider the ratio of volumes . For a large range of R = R(n), we establish a sharp threshold for N, above which as n → ∞, and below which as n → ∞. We also consider the case when is generated by independent random vectors distributed uniformly on the Euclidean sphere. In this case, similar threshold results are proved for both R ∈ (0,1) and...
Volumetric invariants and operators on random families of Banach spaces
The geometry of random projections of centrally symmetric convex bodies in is studied. It is shown that if for such a body K the Euclidean ball is the ellipsoid of minimal volume containing it and a random n-dimensional projection is “far” from then the (random) body B is as “rigid” as its “distance” to permits. The result holds for the full range of dimensions 1 ≤ n ≤ λN, for arbitrary λ ∈ (0,1).
Volumi e proiezioni di corpi convessi
Voroni Diagrams and Arrangements.
Weak and strong moments of random vectors
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.
Weak Distances between Random Subproportional Quotients of
Lower estimates for weak distances between finite-dimensional Banach spaces of the same dimension are investigated. It is proved that the weak distance between a random pair of n-dimensional quotients of is greater than or equal to c√(n/log³n).
Weitere NP-schwere Probleme für minimale Polygonüberdeckungen
Width-integrals and affine surface area of convex bodies.
X-Rays of Polygons.
Zerlegung eines konvexen Polygons in konvexe Polygone.
Zerlegung konvexer Körper durch minimale Trennflächen.
Zerlegungen und Bewertungen von Gitterpolytopen.
Zerlegungsähnlichkeit von Polygonen.
Zonoide und verwandte Klassen konvexer Körper.
Zonoids and conditionally positive definite functions.
Zonoids with an equatorial characterization
It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid...
Zonoids with Minimal Volume-Product.
Zufallspolygone in konvexen Vielecken.
Zum homogenen Ausleuchten konvexer Polytope