Tutte Colloquium - Jane Gao

Title: The rank of random matrices over finite fields

Abstract:

We determine the rank of a random matrix over a finite field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. The proofs are based on the Aizenman-Sims-Starr coupling arguments from mathematical physics.

This work is a collaboration with A. Coja-Oghlan.