A Brunn-Minkowski Inequality for Symplectic Capacities of Convex Domains (2008)
Artstein-Avidan, Shiri, Ostrover, Yaron
In this work, we prove a Brunn–Minkowski-type inequality in the context of symplectic geometry and discuss some of its applications.
A Brunn-Minkowski Inequality for Symplectic Capacities of Convex Domains (2007)
Artstein-Avidan, Shiri, Ostrover, Yaron
In this work we prove a Brunn-Minkowski-type inequality in the context of symplectic geometry and discuss some of its applications.
A two-parameter family of an extension of Beatty sequences (2007)
Shiri Artstein-avidan, Aviezri S. Fraenkel, Vera T. Sós
Beatty sequences ⌊nα + γ ⌋ are nearly linear, also called balanced, namely, the absolute value of the difference D of the number of elements in any two subwords of the same length satisfies D...
The M-ellipsoid, Symplectic Capacities and Volume (2006)
Artstein-Avidan, Shiri, Milman, Vitali D., Ostrover, Yaron
In this work we bring together tools and ideology from two different fields, Symplectic Geometry and Asymptotic Geometric Analysis, to arrive at some new results. Our main result is a...
On Symplectic Capacities and Volume Radius (2006)
Artstein-Avidan, Shiri, Ostrover, Yaron
In this work we discuss a conjecture of Viterbo relating the symplectic capacity of a convex body and its volume. The conjecture states that among all 2n-dimensional convex bodies with a given volume...
Polynomial bounds for large Bernoulli sections of $\ell_1^N$ (2006)
Artstein-Avidan, Shiri, Friedland, Omer, Milman, Vitali, Sodin, Sasha
We prove a quantitative version of the bound on the smallest singular value of a Bernoulli covariance matrix (due to Bai and Yin). Then we use this bound, together with several recent developments,...