Given two sets $A,B\subseteq\R^n$, a measure of their dependence, or correlation, is given by the expected squared inner product between random $x\in A $ and $y\in B$. We prove an inequality showing that no two sets of large enough Gaussian measure (at least $e^{-\delta n}$ for some constant $\delta >0$) ... more >>>

Given an LLL-basis $B$ of dimension $n= hk$ we accelerate slide-reduction with blocksize $k$ to run under a reasonable assjmption in \
$\frac1{6} \, n^2 h \,\log_{1+\varepsilon} \, \alpha $ \
local SVP-computations in dimension $k$, where $\alpha \ge \frac 43$
measures the quality of the ... more >>>

A family of permutations in $S_n$ is $k$-wise independent if a uniform permutation chosen from the family maps any distinct $k$ elements to any distinct $k$ elements equally likely. Efficient constructions of $k$-wise independent permutations are known for $k=2$ and $k=3$, but are unknown for $k \ge 4$. In fact, ... more >>>