Special Probability Seminar

What does a random abelian group look like? Cokernels of random matrices over Z or Z_p provide natural models, and their limits for large matrix size appear in Cohen-Lenstra type heuristics in number theory, topology and combinatorics. They are also direct analogues of singular values in classical random matrix theory. I will discuss results on products of random matrices, where the limit is no longer a random finite group but rather an interacting particle system (the reflecting Poisson sea) describing the evolution of a randomly-growing sequence of groups.