Non-additivity of Renyi entropy and Dvoretzky's Theorem (2009)
Aubrun, Guillaume, Szarek, Stanislaw, Werner, Elisabeth
The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about...
or via WWW, URL: http://www.esi.ac.atDropping a Vertex or a Facet from a Convex Polytope ∗ (2009)
The Erwin, Schrödinger International Boltzmanngasse, Shlomo Reisner, Carsten Schütt, Elisabeth Werner, Shlomo Reisner, ...
UFR de Mathématique
Inequalities for mixed $p$-affine surface area (2008)
We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed $p$-affine surface areas. We introduce a new class of bodies, the illumination surface bodies,...
Uniform estimates for order statistics and Orlicz functions (2008)
Gordon, Yehoram, Litvak, Alexander, Schütt, Carsten, Werner, Elisabeth
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...
Monika Ludwig, Carsten Schütt, Elisabeth Werner, Main Results
There is a constant c such that for every n ∈ N, there is a Nn so that for every N ≥ Nn there is a polytope P in R n with N vertices and where B n 2 voln(B n 2 △P) ≤ c voln(B n 2 2)N n−1
Approximation of the Euclidean ball by polytopes (2008)
Monika Ludwig, Carsten Schütt, Elisabeth Werner, Main Results
There is a constant c such that for every n N, there is a N n so that for every N with N vertices and where B 2 denotes the Euclidean unit ball of dimension n. # partially supported by a grant from...
New $L_p$ Affine Isoperimetric Inequalities (2007)
We prove new $L_p$ affine isoperimetric inequalities for all $ p \in [-\infty,1)$. We establish, for all $p\neq -n$, a duality formula which shows that $L_p$ affine surface area of a convex body $K$...
Szarek, Stanislaw J., Werner, Elisabeth, Zyczkowski, Karol
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely...
Approximation of the Euclidean ball by polytopes (2005)
The Erwin, Schrödinger International Boltzmanngasse, Monika Ludwig, Carsten Schütt, Elisabeth Werner, Monika Ludwig, ...
There is a constant c such that for every n ∈ N there is a Nn so that for every N ≥ Nn there is a polytope P in R n with N vertices and voln(B n 2 △P) ≤ c voln(B n 2 2)N n−1 where B n 2...
Orlicz norms of sequences of random variables (2002)
Gordon, Yehoram, Litvak, Alexander, Schütt, Carsten, Werner, Elisabeth
Let $f_{i}$, $i=1,\dots,n$, be copies of a random variable f and let N be an Orlicz function. We show that for every $x\in \mathbb{R}^{n}$ the expectation $\mathbf{E} \| (x_i f_i) _{i=1}^n \|_N $ is...
An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices (2000)
Ruskai, Mary Beth, Szarek, Stanislaw, Werner, Elisabeth
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any...
Brummelhuis, Raymond, Ruskai, Mary Beth, Werner, Elisabeth
We consider one-dimensional regularizations of the Coulomb potential formed by taking a two-dimensional expectation of the Coulomb potential with respect to the Landau states. It is well-known that...
Study of a Class of Regularizations of 1/|x| using Gaussian Integrals (1999)
Ruskai, Mary Beth, Werner, Elisabeth
This paper presents a comprehensive study of a class of functions which approximate 1/|x| for large x but which are finite at the origin. These functions arise naturally in the study of atoms in...
On the p-affine surface area (1997)
Meyer, Mathieu, Werner, Elisabeth
We give geometric interpretations of certain affine invariants of convex bodies. The affine invariants are the p-affine surface areas introduced by Lutwak. The geometric interpretations involve...
A pair of optimal inequalities related to the error function (1997)
Ruskai, M. Beth, Werner, Elisabeth
The Error Function \begin{eqnarray} V(x) & \equiv & \sqrt{\pi} e^{x^2} [1 - \hbox{erf}(x)] \\ & = & \int_0^\infty \frac{ e^{-u} }{\sqrt{x^2 + u}} du = 2 e^{x^2}\int_x^\infty e^{-t^2} dt \nonumber...
The Santalo-regions of a convex body (1997)
Meyer, Mathieu, Werner, Elisabeth
Motivated by the Blaschke-Santal\'o inequality, we define for a convex body K in ${\bf R}^n$ and for $t \in {\bf R}$ the Santal\'o-regions S(K,t) of K. We investigate properties of these sets and...
A general geometric construction for affine surface area (1997)
Let $K$ be a convex body in ${\bf R}^n$ and $B$ be the Euclidean unit ball in ${\bf R}^n$. We show that $$\mbox{lim}_{t\rightarrow 0} \frac{|K| -|K_t|}{|B| - |B_t|}= \frac{as(K)}{as(B)},$$ where...
Szarek, Stanislaw J., Werner, Elisabeth
Let $\mu$ be a Gaussian measure (say, on ${\bf R}^n$) and let $K, L \subset {\bf R}^n$ be such that K is convex, $L$ is a "layer" (i.e. $L = \{x : a \leq < x,u > \leq b \}$ for some $a$, $b \in {\bf...
Stanislaw Szarek And, Stanislaw J. Szarek, Elisabeth Werner
. Let ¯ be a Gaussian measure (say, on R n ) and let K;L ` R n be such that K is convex, L is a "layer" (i.e. L = fx : a hx; ui bg for some a, b 2 R and u 2 R n ) and the centers of mass...
A Pair of Optimal Inequalities Related to the Error Function (1997)
Mary Beth Ruskai, Elisabeth Werner
(4) We also show that these inequalities are optimal for functions of the form (4) with equality only at g ß (0) = V (0) = p ß: The bounds in (3) are considerably sharper than the classical...
A Nonsymmetric Correlation Inequality for Gaussian Measure
Szarek, Stanislaw J., Werner, Elisabeth
Let[mu]be a Gaussian measure (say, onRn) and letK,L[subset, double equals]Rnbe such thatKis convex,Lis a "layer" (i.e.,L={x:Â a[less-than-or-equals, slant][less-than-or-equals, slant]b} for...