Federico Camia (Amsterdam)

Connectivity Phase Transitions in Fractal Percolation Models

vendredi 29 janvier 2010, 13h30 - 14h30

Salle de réunion, espace Turing

Mandelbrot’s percolation is a multidimensional, stochastic
generalization of the Cantor ternary set. It generates random
fractal sets whose connectivity properties change as a parameter
is varied. After introducing the model and various known results,
I will present some new results and work in progress concerning
crossing probabilities, dimensionality and Holder continuity for
the random sets generated by Mandelbrot’s percolation. If time
permits, I will introduce some other models of fractal percolation
that present similar features.
(Based on joint work with E. Broman, and with Broman, M. Joosten
and R. Meester.)