Bourgain’s discretization theorem asserts that there exists a universal constant C∈(0,∞) with
the following property. Let X, Y be Banach spaces with dim X= n. Fix D∈(1,∞) and set δ= e…

In this work, we study the volume ratio of the projective tensor products ℓ p n ⊗ π ℓ q n ⊗ π ℓ
r n with 1 ≤ p ≤ q ≤ r ≤ ∞ . We obtain asymptotic formulas that are sharp in almost all …

It is shown that if (X,||.||_X) is a Banach space with Rademacher type p \ge 1, then for every
integer n there exists an even integer m < Cn^{2-1/p}log n (C is an absolute constant), such …

It is shown that if (X,‖⋅‖ X ) is a Banach space with Rademacher cotype q then for every
integer n there exists an even integer m≲n 1+1q such that for every f:Z m n →X we have …

While global convergence of the Douglas–Rachford iteration is often observed in
applications, proving it is still limited to convex and a handful of other special cases. Lyapunov …

Bourgain's discretization theorem asserts that there exists a universal constant $C\in (0,\infty)$
with the following property. Let $X,Y$ be Banach spaces with $\dim X=n$. Fix $D\in (1,\…

This note contains two types of small ball estimates for random vectors in finite-dimensional
spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball …

Given a compact star-shaped domain $$K\subseteq \mathbb {R}^d$$ K ⊆ R d , n vectors $$v_1,\ldots
,v_n \in \mathbb {R}^d$$ v 1 , … , v n ∈ R d , a number $$R>0$$ R > 0 , and iid …

… BORWEIN and OHAD GILADI … Giladi … OHAD GILADI, Centre for Computer-assisted
Research Mathematics and its Applications (CARMA), …

Let $T$ be an $n\times n$ random matrix, such that each diagonal entry $T_{i, i}$ is a
continuous random variable, independent from all the other entries of $T$. Then for every $n\times …