Random matrices: Law of the determinant.

Let $M_n$ be a random matrix with iid entries with mean zero and variance one. The determinant $det M_n$ is an important parameter which has been studied for a long time. In this talk, we focus on the limiting distribution and prove that the logarithm of $|det M_n|$ satisfies a central limit theorem.

For simplicity, we will mainly consider the case when the entries are Bernoulli random variables; the proof extends easily to the general case.