Is there a well-known PDF/CDF of the Nearest Neighbor to the Nearest Neighbor of the origin. Specifically, assume we have a homogeneous Poisson Point Process (HPPP), $\Phi\in\mathbb{R}^2$. For the ease of exposition, let $X$ be the nearest point to the origin, and $Y$ as the nearest point to X, where $X,Y \in \Phi$. Then, what's the PDF/CDF of the distance between X and Y?
If there's no well-known PDF/CDF, can you kindly advise me the steps to obtain them. So far, I only know the PDF and CDF of the distance between X and the origin.