Surjectivity of random integral matrices on integral vectors

Probability Seminar
Mar 11, 2020 3:10pm to 4:00pm
330 Evans Hall
Happening As Scheduled
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...
Melanie Matchett Wood, U.C. Berkeley