3 problems

Let $N=(n_1,\dots,n_n)$ be a multinomial vector with parameter $n$ and probabilities $(n^{-1},\dots,n^{-1})$. For each $C>0$, let $c>0$ be a constant independent of $n$ such that t…

Multivariate threshold conjecture. The optimal thresholds for exact and almost exact recovery are, respectively,

Dimension-dependent threshold conjecture. The conclusion of the main theorem for the sublinear regime $d=o(n)$ no longer holds when $d=\rho n$, and the sharp threshold depends on…