no code implementations • 23 May 2024 • Ainesh Bakshi, Pravesh Kothari, Goutham Rajendran, Madhur Tulsiani, Aravindan Vijayaraghavan
A set of high dimensional points $X=\{x_1, x_2,\ldots, x_n\} \subset R^d$ in isotropic position is said to be $\delta$-anti concentrated if for every direction $v$, the fraction of points in $X$ satisfying $|\langle x_i, v \rangle |\leq \delta$ is at most $O(\delta)$.
no code implementations • 6 Sep 2022 • Goutham Rajendran, Madhur Tulsiani
Using our general framework, we derive bounds for "sparse graph matrices", which were obtained only recently by Jones et al. [FOCS 2021] using a nontrivial application of the trace power method, and was a core component in their work.