We determine the distribution of the sandpile group (or Jacobian) of the Erdős-Rényi
random graph $ G (n, q) $ as $ n $ goes to infinity. We prove the distribution converges to a …

We present a heuristic that suggests that ranks of elliptic curves E over Q are bounded. In
fact, it suggests that there are only finitely many E of rank greater than 21. Our heuristic is …

We prove that the $2^\infty $-class groups of the imaginary quadratic fields have the
distribution predicted by the Cohen-Lenstra heuristic. Given an elliptic curve E/Q with full …

For random integer matrices M 1,…, M k∈ Mat n (Z) with independent entries, we study the
distribution of the cokernel Cok (M 1⋯ M k) of their product. We show that this distribution …

In this paper we study the cokernels of various random integral matrix models, including
random symmetric, random skew-symmetric, and random Laplacian matrices. We provide a …

The moment problem in probability theory asks for criteria for when there exists a unique
measure with a given tuple of moments. We study a variant of this problem for random …

We study the distribution of the sandpile group of random $ d $-regular graphs. For the
directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting …

We consider the probability theory, and in particular the moment problem and universality
theorems, for random groups of the sort that arise or are conjectured to arise in number …

We study the distribution of singular numbers of products of certain classes of pp‐adic
random matrices, as both the matrix size and number of products go to∞ ∞ simultaneously …

In this paper, we make specific conjectures about the distribution of Jacobians of random
graphs with their canonical duality pairings. Our conjectures are based on a Cohen–Lenstra …