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.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
The ACO Seminar (2018–2019)