Exiting measures for random walks on infinite rooted trees

Abstract

We consider conformal iterated function systems (CIFS) that are induced by an infinite rooted tree TT, which we call TT-conformal iterated function systems (TT-CIFS). We focus on the parameterized families of TT-CIFS that satisfy the trasversality condition and give a dimension formula for the exiting measure for a.e. parameter. We also give a sufficient condition that the exiting measure is absolutely continuous for a.e. parameter.

Keywords

• iterated function systems
• random walks
• dimensions
• 28dxx
• 37hxx