Zobrazeno 1 - 10
of 84
pro vyhledávání: '"SZAREK, STANISŁAW"'
Autor:
Szarek, Stanislaw, Wolff, Pawel
The celebrated Dvoretzky theorem asserts that every $N$-dimensional convex body admits central sections of dimension $d = \Omega(\log N)$, which is nearly spherical. For many instances of convex bodies, typically unit balls with respect to some norm,
Externí odkaz:
http://arxiv.org/abs/2410.15118
We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sided bounds for deviation from the median as well as from the mean. For
Externí odkaz:
http://arxiv.org/abs/2406.13581
Autor:
Bombiak, Edyta, Szarek, Stanisław
Publikováno v:
Journal of Modern Science. 50(1):258-274
Externí odkaz:
https://www.ceeol.com/search/article-detail?id=1130654
Publikováno v:
Front. Appl. Math. Stat., 28 May 2019
In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low rankness. In
Externí odkaz:
http://arxiv.org/abs/1904.07893
Publikováno v:
Commun. Math. Phys. 375, 679-724 (2020)
We define and study XOR games in the framework of general probabilistic theories, which encompasses all physical models whose predictive power obeys minimal requirements. The bias of an XOR game under local or global strategies is shown to be given b
Externí odkaz:
http://arxiv.org/abs/1809.10616
The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the results by St{\o}rmer and Woronowicz from 1960s and 1970s settling the low dimensional cases. By duali
Externí odkaz:
http://arxiv.org/abs/1512.03293
Autor:
Aubrun, Guillaume, Szarek, Stanislaw
Publikováno v:
Discrete Analysis, 2017:1, 20 pp
The well-known Horodecki criterion asserts that a state $\rho$ on $\mathbf{C}^d \otimes \mathbf{C}^d$ is entangled if and only if there exists a positive map $\Phi : \mathsf{M}_d \to \mathsf{M}_d$ such that the operator $(\Phi \otimes \mathrm{Id})(\r
Externí odkaz:
http://arxiv.org/abs/1510.00578
Publikováno v:
Scientific Papers of Silesian University of Technology. Organization & Management / Zeszyty Naukowe Politechniki Slaskiej. Seria Organizacji i Zarzadzanie; 2024, Issue 198, p655-678, 24p
Publikováno v:
Phys. Rev. A 90, 012301 (2014)
Following recent work of Beigi and Shor, we investigate PPT states that are "heavily entangled." We first exploit volumetric methods to show that in a randomly chosen direction, there are PPT states whose distance in trace norm from separable states
Externí odkaz:
http://arxiv.org/abs/1309.7992
Autor:
Szarek, Stanislaw J.
We consider the following measure of symmetry of a convex n-dimensional body K: $\rho(K)$ is the smallest constant for which there is a point x in K such that for partitions of K by an n-1-dimensional hyperplane passing through x the ratio of the vol
Externí odkaz:
http://arxiv.org/abs/1302.2076