Random Polytopes in the d- Dimensional Cube.
Random Projections of Regular Simplices.
Random system of lines in the Euclidean plane .
Random walks that avoid their past convex hull.
Random ε-nets and embeddings in
We show that, given an n-dimensional normed space X, a sequence of independent random vectors , uniformly distributed in the unit ball of X*, with high probability forms an ε-net for this unit ball. Thus the random linear map defined by embeds X in with at most 1 + ε norm distortion. In the case X = ℓ₂ⁿ we obtain a random 1+ε-embedding into with asymptotically best possible relation between N, n, and ε.
Randomness and pattern in convex geometric analysis.
Rareté des intervalles recouvrant un point dans un recouvrement aléatoire
Räumliche Zindlerkurven.
Real analytic convex surfaces with positive topological entropy and rigid body dynamics.
Recognizing sets by means of some of their sections.
Reconstructing dimensions of intersections of convex sets.
Reconstructing Plane Sets from Projections.
Reduced spherical polygons
For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We...
Redundance of vertices of the cube relatively to its minimal ellipsoid.
Reflexivity of convex subsets of L(H) and subspaces of .
Regular polygons
Regular positive bases
Regular Simplices and Gaussian Samples.
Regularization of star bodies by random hyperplane cut off
We present a general result on regularization of an arbitrary convex body (and more generally a star body), which gives and extends global forms of a number of well known local facts, like the low M*-estimates, large Euclidean sections of finite volume-ratio spaces and others.
Relative extreme subsets