Por Jamerson Douglas Bezerra (Nicolaus Copernicus University).

In the context of dynamically defined Schrodinger operators, the Thouless formula provides a strong relation between the behaviour of the Lyapunov exponent of the associated Schrodinger cocycle and the distribution measure of the elements of the almost sure spectrum - the integrated density of states (IDS). Indeed, this formula is the essential tool to translate the regularity properties of the Lyapunov expoent to the IDS.
In this talk we are going to discuss how to generalize this formula for winding family of affine cocycles and how to use it to obtain information concerning the regularity of the Lyapunov exponents of random cocycles.