Bowen's formula and the difference between random iterated function systems and random recursive constructions

In this paper, we show that the difference in independence structures between random iterated function systems and random recursive constructions is reflected in the validity of Bowen’s formula. More precisely, we construct random iterated function systems for which Bowen’s formula fails, whereas Bowen’s formula always holds for random recursive constructions. Our construction demonstrates that the difference in independence structures between the two random models has genuine consequences for dimension theory.