Scientists are exploring a mysterious pattern, found in birds’ eyes, boxes of marbles and other surprising places, that is neither regular nor random. All complex correlated systems, from Arctic melt ...

We place ourselves in the setting of high-dimensional statistical inference where the number of variables p in a dataset of interest is of the same order of magnitude as the number of observations n.

We prove that given any 𝜖 > 0, random integral 𝑛 × 𝑛 matrices with independent entries that lie in any residue class modulo a prime with probability at most 1 − 𝜖 have cokernels asymptotically (as ...