Lattice coverings and gaussian measures of n-dimensional convex bodies

W. Banaszczyk, Stanislaw J. Szarek

Let $\Vert \cdot \Vert$ be the euclidean norm on ${\mathbf{R}}^n$ and ${\gamma }_n$ the (standard) Gaussian measure on ${\mathbf{R}}^n$ with density $(2\pi {)}^{-n/2}{e}^{-\Vert x{\Vert }^2/2}$. Let $\vartheta$ ($ \s…