Luc Devroye

Finding Adam in noisy trees

It is proved that, as long as $p=o(\log n /n)$, for any $\varepsilon>0$, one can construct a confidence set of vertices of size $K(\varepsilon)$ that depends only on $\varepsilon$ and not on $n$, such that it contains the root with probability at least $1-\varepsilon$.