On the Hausdorff Dimension of Bernoulli Convolutions

Add to your list(s) Download to your calendar using vCal

• Dr. Tom Kempton (University of Manchester)
• Thursday 28 February 2019, 13:00-14:00
• Lecture Room C, Watson Building.

If you have a question about this talk, please contact Tony Samuel.

Bernoulli convolutions are a simple family of self-similar measures with overlaps. The problem of determining which parameters give rise to Bernoulli convolutions of dimension one has been studied since the 1930s, and is still far from being completely solved. For algebraic parameters, we show how to give an expression for the dimension of the Bernoulli convolution in terms of random products of matrices, allowing us to conclude that the Bernoulli convolution has dimension one in many examples where the dimension was previously unknown. The problem has close connections to some problems in random dynamical systems, and yet we don’t really know best how to exploit these connections. This is joint work with Shigeki Akiyama, De-Jun Feng and Tomas Persson.

This talk is part of the Topology and Dynamics seminar series.

This talk is included in these lists:

• Lecture Room C, Watson Building
• School of Mathematics events
• Topology and Dynamics seminar

Note that ex-directory lists are not shown.