Zobrazeno 1 - 10
of 554
pro vyhledávání: '"A. Alonso Gutiérrez"'
Borell's inequality states the existence of a positive absolute constant $C>0$ such that for every $1\leq p\leq q$ $$ \left(\mathbb E|\langle X, e_n\rangle|^p\right)^\frac{1}{p}\leq\left(\mathbb E|\langle X, e_n\rangle|^q\right)^\frac{1}{q}\leq C\fra
Externí odkaz:
http://arxiv.org/abs/2407.18235
A classical inequality by Gr\"unbaum provides a sharp lower bound for the ratio $\mathrm{vol}(K^{-})/\mathrm{vol}(K)$, where $K^{-}$ denotes the intersection of a convex body with non-empty interior $K\subset\mathbb{R}^n$ with a halfspace bounded by
Externí odkaz:
http://arxiv.org/abs/2404.08319
We consider the problem of finding the best function $\varphi_n:[0,1]\to\mathbb{R}$ such that for any pair of convex bodies $K,L\in\mathbb{R}^n$ the following Brunn-Minkowski type inequality holds $$ |K+_\theta L|^\frac{1}{n}\geq\varphi_n(\theta)(|K|
Externí odkaz:
http://arxiv.org/abs/2211.17069
In this paper we study various Rogers-Shephard type inequalities for the lattice point enumerator $\mathrm{G}_{n}(\cdot)$ on $\mathbb{R}^n$. In particular, for any non-empty convex bounded sets $K,L\subset\mathbb{R}^n$, we show that \[\mathrm{G}_{n}(
Externí odkaz:
http://arxiv.org/abs/2111.11533
We prove several estimates for the volume, mean width, and the value of the Wills functional of sections of convex bodies in John's position, as well as for their polar bodies. These estimates extend some well-known results for convex bodies in John'
Externí odkaz:
http://arxiv.org/abs/2012.10166
Autor:
Pablo Martínez-Arellano, Jorge L. Balderrama-Bañares, Alonso Gutiérrez-Romero, Diego López-Mena
Publikováno v:
Revista Mexicana de Neurociencia, Vol 25, Iss 5 (2024)
Externí odkaz:
https://doaj.org/article/394f49788768491f86e06f2ac25d0651
In this paper, we study the asymptotic thin-shell width concentration for random vectors uniformly distributed in Orlicz balls. We provide both asymptotic upper and lower bounds on the probability of such a random vector $X_n$ being in a thin shell o
Externí odkaz:
http://arxiv.org/abs/2011.07523
Lasserre [La] proved that for every compact set $K\subset\mathbb R^n$ and every even number $d$ there exists a unique homogeneous polynomial $g_0$ of degree $d$ with $K\subset G_1(g_0)=\{x\in\mathbb R^n:g_0(x)\leq 1\}$ minimizing $|G_1(g)|$ among all
Externí odkaz:
http://arxiv.org/abs/2007.07952
Having its origin in theoretical computer science, the Kannan-Lov\'asz-Simonovits (KLS) conjecture is one of the major open problems in asymptotic convex geometry and high-dimensional probability theory today. In this work, we establish a new connect
Externí odkaz:
http://arxiv.org/abs/2003.11442
We prove various extensions of the Loomis-Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors $w_i$ of a not necessarily orthonormal basis of $\mathbb{R}^n$, or thei
Externí odkaz:
http://arxiv.org/abs/2002.05794