arXiv subjects

Yehoram Gordon

Publications and source records attributed to Yehoram Gordon.

4 recordsLinked to original sources

arXiv2013

Large distortion dimension reduction using random variable

Consider a random matrix $H:\mathbb{R}^n\longrightarrow\mathbb{R}^m$. Let $D\geq2$ and let $\{W_l\}_{l=1}^{p}$ be a set of $k$-dimensional affine subspaces of $\mathbb{R}^n$. We ask what is the probability that for all $1\leq l\leq p$ and $x,y\in W_l$, \[ \|x-y\|_2\leq\|Hx-Hy\|_2\leq D\|x-y\|_2. \] We show that for $m=O\big(k+\frac{\ln{p}}{\ln{D}}\big)$ and a variety of different classes of random matrices $H$, which include the class of Gaussian matrices, existence is assured and the probability is very high. The estimate on $m$ is tight in terms of $k,p,D$.

math.FA↗

arXiv2008

Uniform estimates for order statistics and Orlicz functions

We establish uniform estimates for order statistics of sequences of independent identically distributed random variables with log-concave distribution in terms of Orlicz norms associated with the distribution function of the random variables.

math.PR↗

arXiv1997

The relations between volume ratios and new concepts of gl constants

In this paper we investigate a property named GL(p,q) which is closely related to the Gordon-Lewis property. Our results on GL(p,q) are then used to estimate volume ratios relative to $\ell_p$, $1<p \le\infty$, of unconditional direct sums of Banach spaces.

math.FA↗

arXiv1996

Umbrellas and polytopal approximation of the euclidean ball

There are two positive, absolute constants $c_{1}$ and $c_{2}$ so that the volume of the difference set of the $d$-dimensional Euclidean ball and an inscribed polytope with n vertices is larger than $$ c_{2}\ d\ {n}^{-\frac{2}{d-1}}vol_d(B^d_2) $$ for $n \geq (c_{1}\ d)^{\frac{d-1}{2}}$.

math.MG↗