Event time:
Tuesday, April 22, 2014 - 12:00pm to 1:00pm
Location:
AKW 200
Speaker:
Jacques Peyriere
Speaker affiliation:
Université Paris-Sud (France)
Event description:
The Mandelbrot cascade constructed from a random variable W of expectation 1, when non degenerate, provides a new variable Y of expectation 1. The law of Y depends only on the law of W, so Mandelbrot cascades can be viewed as a mapping T from probability distributions to probability distributions. Starting from a suitable distribution, this mapping can be iterated. This gives rise to a Central Limit Theorem.
When dealing with Mandelbrot cascades in a random environment new phenomena occur. One has to distinguish two regimes:
1) The conservative case for which there is a CLT, which can be non-standard.
2) In the non-conservative case the map T has a unique fixed point which is also a fixed point of some kind of smoothing transformation.