# Event detail

## Surjectivity of random integral matrices on integral vectors

Seminar: Probability Seminar | March 11 | 3:10-4 p.m. | 330 Evans Hall

Melanie Matchett Wood, U.C. Berkeley

A random n by m matrix gives a random linear transformation

from \Z^m to \Z^n (between vectors with integral coordinates). Asking for the probability that such a map is injective is a question of the non-vanishing of determinants. In this talk, we discuss the

probability that such a map is surjective, which is a more subtle

integral question. We show that when m=n+u, for u at least 1, as n

goes to infinity, the surjectivity probability is a non-zero product

of inverse values of the Riemann zeta function. This probability is

universal, i.e. we prove that it does not depend on the distribution

from which you choose independent entries of the matrix. This talk is

on joint work with Hoi Nguyen.

510-000-0000