Leírás
To model turbulence, Mandelbrot introduced a family of statistically self-similar random sets E which is now called fractal percolation or Mandelbrot percolation. This is a two-parameter (M,p) family of random sets in R^d , where M ≥ 2 is an integer and 0 < p < 1 is a probability. The inductive construction of E is as follows. The closed unit cube of R^d is divided into M^d congruent cubes. Each of them is retained with probability p and discarded with probability 1−p. In the retained cubes, we repeat this division and retaining/discarding process independently of everything ad infinitum or until there are no retained cubes left. The random set E that remains after infinitely many steps (formally: the intersection of the unions of retained cubes on all construction stages) is the fractal percolation set.
Using an analogous method, we define more general random fractals and study their orthogonal projections to straight lines from the point of Hausdorff dimension, the positivity of Lebesgue measure and the existence of interior points.
All the new results are joint with Vilma Orgoványi.
ZOOM link:
https://zoom.us/j/97594629945?pwd=MmFNaVk4a1FhdjEvc2RRdGdod0FpZz09
Meeting ID: 975 9462 9945
Passcode: 767601