2 problems

Nonlinear $p$-stable projection conjecture. With probability at least $1-N^{-(c-2)}$, for all $x,y\in P$, if $\lVert x-y\rVert_p=O(\epsilon^2)$ then

Let $P\subset\mathbb{R}^D$ be a set of $N$ points, let $0<\epsilon\leq 1/4$, and let $c\geq 3$. Let $F:\mathbb{R}^D\to\mathbb{R}^k$ be the Cauchy random projection and let $\rho$ a…