منابع مشابه
Randomized Isomorphic Dvoretzky Theorem
Let K be a symmetric convex body in IR for which B 2 is the ellipsoid of minimal volume. We provide estimates for the geometric distance of a “typical” rank n projection of K to B 2 , for 1 ≤ n < N . Known examples show that the resulting estimates are optimal (up to numerical constants) even for the Banach–Mazur distance. Résumé French title here Soit K un corps convexe symétrique de IR dont l...
متن کاملOn the Dvoretzky–wald–wolfowitz Theorem on Nonrandomized Statistical Decisions∗
The result by Dvoretzky, Wald, and Wolfowitz on the sufficiency of nonrandomized decision rules for statistical decision problems with nonatomic state distributions holds for arbitrary Borel decision sets and for arbitrary measurable loss functions.
متن کاملScale-oblivious Metric Fragmentation and the Nonlinear Dvoretzky Theorem
We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is D-equivalent to an ultrametric, where D ∈ (2,∞) is a prescribed target distortion. Since this procedure works for D arbitrarily close to the nonlinear Dvoretzky phase transition at distortion 2, we thus obtain a much simpler probabilistic pro...
متن کامل00 9 Topological Aspects of the Dvoretzky Theorem
We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
متن کاملAN \ ISOMORPHIC " VERSION OF DVORETZKY ' S THEOREM , IIby
A diierent proof is given to the result announced in MS2]: For each 1 k < n we give an upper bound on the minimal distance of a k-dimensional subspace of an arbitrary n-dimensional normed space to the Hilbert space of dimension k. The result is best possible up to a multiplicative universal constant. Our main result is the following extension of Dvoretzky's theorem (from the range 1 < k < c log...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1984
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500022203