Modul:   MAT971  Stochastische Prozesse

Singularity of random Bernoulli matrices

Vortrag von Prof. Dr. Konstantin Tikhomirov

Datum: 12.05.21  Zeit: 17.15 - 19.00  Raum:

For each n, let Bn be an n-by-n matrix with i.i.d. entries taking values +1 and -1. We show that the probability that Bn is singular, is of order (1/2+o(1))^n, where the quantity o(1) converges to zero as n grows to infinity. We shall further discuss a variation of the problem for sparse Bernoulli matrices, and give an overview of the recent progress in this line of research.