Exact Hausdorff measure of random self-similar code-trees with necks

Fractal Geometry and Dynamics

28 November 15:00 - 15:50

Sascha Troscheit - University of Waterloo

The s-dimensional Hausdorff measure of many randomly constructed sets is almost surely 0 for the ‘correct' exponent s. For stochastic self-similar sets this follows easily by considering the most natural coverings and some argument involving positive variance of the random Hutchinson-Moran sum. Instead, research focussed on modifying the definition of the Hausdorff measure by finding gauge functions under which one obtains positive and finite measure. In this talk I will give some background on the random recursive case and then consider the model of random code-trees with necks which include the random homogeneous and V-variable model.
Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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