Seminar
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.
Organizers
Kenneth 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