6 problems

Fulman's conjecture. For general $alphage 1$, the correct bound for this Kolmogorov distance is a universal constant multiplied by

Consider the number of $k$-faces of the convex hull of a Poisson point process in a smooth convex body, and let the established Berry–Esseen rate for the first layer be … The $n$-t…

High-dimensional Berry–Esseen rate conjecture. The best possible dependence on the sample size in the high-dimensional Berry–Esseen bound should be of order $n^{-1/6}$.

Let $d$ denote the dimension and $n$ the sample size. Suppose the dimension grows at the scaling … The authors conjecture that this scaling cannot be weakened while retaining the p…

Logarithmic-factor removal conjecture. The factor $ln n$ in these two bounds can be removed, so that the right-hand sides become $C/\sqrt{n}$.

Bentkus's conjecture. The best constant factor in the nonuniform Berry–Esseen bound remains $1$ for all $n$ when the factor $1+z^3$ is replaced by $z^3$.