Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Antonis Tsolomitis"'
Publikováno v:
TUGboat. 43:351-362
Publikováno v:
TUGboat. 42:166-169
Publikováno v:
Advances in Applied Mathematics. 75:116-143
Let $x_1,\ldots ,x_N$ be independent random points distributed according to an isotropic log-concave measure $\mu $ on ${\mathbb R}^n$, and consider the random polytope $$K_N:={\rm conv}\{ \pm x_1,\ldots ,\pm x_N\}.$$ We provide sharp estimates for t
Publikováno v:
Proceedings of the American Mathematical Society. 144:763-773
A classical inequality of Rogers and Shephard states that if K is a centered convex body of volume 1 in Rn then 1 6 g(K, k;F ) := ( volk(PF (K)) voln−k(K ∩ F⊥) )1/k 6 (n k )1/k 6 cn k for every F ∈ Gn,k, where c > 0 is an absolute constant. W
Publikováno v:
Transactions of the American Mathematical Society. 367:4569-4593
We study some geometric properties of the L q L_q -centroid bodies Z q ( μ ) Z_q(\mu ) of an isotropic log-concave measure μ \mu on R n {\mathbb R}^n . For any 2 ⩽ q ⩽ n 2\leqslant q\leqslant \sqrt {n} and for ε ∈ ( ε 0 ( q , n ) , 1 ) \var
Publikováno v:
Journal of Functional Analysis. 257:2820-2839
Let K be an isotropic convex body in R n and let Z q ( K ) be the L q -centroid body of K. For every N > n consider the random polytope K N : = conv { x 1 , … , x N } where x 1 , … , x N are independent random points, uniformly distributed in K.
Publikováno v:
ASSETS
The TeX/LaTeX typesetting system is the most widespread system for creating documents in Mathematics and Science. However, no reliable tool exists to this day for automatically transcribing documents from the above formats into Braille code. Thus, bl
Publikováno v:
Journal of the London Mathematical Society. 72:779-798
The paper considers three questions about independent random points uniformly distributed in isotropic symmetric convex bodies $K, T_1,\ldots, T_s$ . (a) Let $\varepsilon\,{\in}\, (0,1)$ and let $x_1,\ldots, x_N$ be chosen from K . Is it true that if
Publikováno v:
Journal of Functional Analysis. 223(1):86-108
Sharpening work of the first two authors, for every proportion λ∈(0,1) we provide exact quantitative relations between global parameters of n-dimensional symmetric convex bodies and the diameter of their random ⌊λn⌋-dimensional sections. Usin
Publikováno v:
Geometriae Dedicata. 84:63-79
We provide a generalization of John's representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in ℝ n . From this representation we obtain Banach–Mazur distance and volume rati