2019/07/17 by Uta Freiberg, Freiberg, Uta, Stefan Kohl +1
Mathematics · Physics and Astronomy · #28A80 #31C35 #60J10 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1907.07499
openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We want to consider fractals generated by a probabilistic iterated function scheme with open set condition and we want to interpret the probabilities as weights for every part of the fractal. In the homogenous case, where the weights are not taken into account, Denker and Sato introduced in 2001 a Markov chain on the word space and proved, that the Martin boundary is homeomorphic to the fractal set. Our aim is to redefine the transition probability with respect to the weights and to calculate the Martin boundary. As we will see, the inhomogenous Martin boundary coincides with the homogenous case.