PRODUCTS OF RANDOM MATRICES

Abstract

In the first part, we study the behaviour of products of independent and identically distributed random matrices with distribution μ. We will give the proofs that under certain assumptions the action of the random matrices on the projective space admit a unique invariant measure. We then give the proofs of Law of Large Numbers, Central Limit Theorem, and Local Limit Theorem. In the second part of the thesis, we investigate the action of the random matrices on a positive closed (1,1)-current on the complex projective space. We introduce a stationary current associated to μ, then we prove an equidistribution towards this stationary current.