abstract: We will describe invariant densities for any random system of piecewise linear maps that are expanding on average. More precisely, we provide a procedure to obtain an explicit formula for the density of an absolutely continuous invariant measure. This result generalises the method of Kopf (1990), valid in the deterministic setting. We conclude showing how this construction merges the results by Kempton (2014) and Suzuki (2017) on random β-transformations.
Joint work with C. Kalle.