How fractal is the sum of two random fractals?

Stochastic Analysis Seminar Series

Let C and C’  be two Cantor sets, with Hausdorff dimensions d and d’. Their algebraic sum C+C’ will in general be much “fatter” than C or C’. Here C+C’ is the set of all x+y, where x is from C and y from C’. Motivated by his studies of diffeomorphisms, Palis conjectured that generically it should be true that d+d’ > 1 should imply that C+C’ contains an interval. We consider this conjecture in a probabilistic context, where ‘generically’ means ‘almost surely’, for various definitions of random Cantor sets.

Location:
Speaker(s):

Michel Dekking (Delft University of Technology)

Date:
Monday, January 30, 2012 - 14:15
to 15:15