Absolute continuity for random iterated function systems with overlaps

Yuval Peres, Károly Simon, Boris Solomyak

We consider linear iterated function systems with a random multiplicative error on the real line. Our system is $\{x\mapsto d_i+{\lambda }_{i}Yx{\}}_{i=1}^m$, where $d_i\in \mathbb{R}$ and ${\lambda }_i>0$…