Balazs Barany (TU Budapest):
Almost multiplicativity of planar matrix cocycles and the difference between quasi-Bernoulli and Gibbs measures.
Abstract: In the dimension theory of self-affine sets, in the thermodynamic formalism of linear cocycles, and in the theory of random matrix products, it has often been found useful to assume almost multiplicativity of the norm of matrix products in order to simplify or make feasible certain types of calculation. For example, matrices with strictly positive entries have this property. In this talk, we present an equivalent condition for the almost multiplicativity of the norm of the products of 2x2 matrices. As an application, we show that there exists a shift-invariant, ergodic quasi-Bernoulli measure, which is not Gibbs with respect to any continuous potential function. This is a joint work with Antti Käenmäki and Ian D. Morris.