Noela Müller (TU/e)

Introduction & sparse random matrices

In this talk, I will introduce myself and give an overview of my research interests. The second half is dedicated to ongoing work on a full rank condition for sparse random matrices: For a broad range of sparse random matrix models, we provide a sufficient condition on the parameters for the resulting matrix to be of full (row) rank w.h.p. This criterion generalises a number of prior results. In particular, it supplies a generalisation of the satisfiability threshold theorem for a very well known random constraint satisfaction problem, the random k-XORSAT problem. Our main theorem also covers other important applications, including random matrix models on which low-density parity check codes rely.