Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Bastero, Jesús"'
We show that for any $1\leq p\leq\infty$, the family of random vectors uniformly distributed on hyperplane projections of the unit ball of $\ell_p^n$ verify the variance conjecture $$ \textrm{Var}\,|X|^2\leq C\max_{\xi\in S^{n-1}}\mathbb{E}\langle X,
Externí odkaz:
http://arxiv.org/abs/1610.04023
We show that any random vector uniformly distributed on any hyperplane projection of $B_1^n$ or $B_\infty^n$ verifies the variance conjecture $$\text{Var}|X|^2\leq C\sup_{\xi\in S^{n-1}}\E^2\E|X|^2.$$ Furthermore, a random vector uniformly dis
Externí odkaz:
http://arxiv.org/abs/1209.4270
We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp) connection betw
Externí odkaz:
http://arxiv.org/abs/1107.2139
The isotropy constant of any $d$-dimensional polytope with $n$ vertices is bounded by $C \sqrt{n/d}$ where $C>0$ is a numerical constant.
Externí odkaz:
http://arxiv.org/abs/0904.2632
We consider $k$-dimensional central sections of the unit ball of $\ell_p^n$ (denoted $B_p^n$) and we prove that their volume are bounded by the volume of $B_p^n$ whenever $1
Externí odkaz:
http://arxiv.org/abs/math/0008007
Publikováno v:
Proceedings of the American Mathematical Society, 2000 Nov 01. 128(11), 3329-3334.
Externí odkaz:
https://www.jstor.org/stable/2668669
Publikováno v:
Proceedings of the American Mathematical Society, 2000 Jan 01. 128(1), 65-74.
Externí odkaz:
https://www.jstor.org/stable/119385
The classical Brunn-Minkowski inequality states that for $A_1,A_2\subset\R^n$ compact, $$ |A_1+A_2|^{1/n}\ge |A_1|^{1/n}+|A_2|^{1/n}\eqno(1) $$ where $|\cdot|$ denotes the Lebesgue measure on $\R^n$. In 1986 V. Milman {\bf [Mil 1]} discovered that if
Externí odkaz:
http://arxiv.org/abs/math/9501210
In this note we investigate some aspects of the local structure of finite dimensional $p$-Banach spaces. The well known theorem of Gluskin gives a sharp lower bound of the diameter of the Minkowski compactum. In [Gl] it is proved that diam$({\cal M}_
Externí odkaz:
http://arxiv.org/abs/math/9209213