# סמינר תלמידי מחקר - אריאל רפפורט

Title: Bernoulli convolutions and Erdős's argument for singularity
Abstract: Given $0<\lambda<1$ the Bernoulli convolution corresponding to the parameter $\lambda$ is the distribution $\mu_{\lambda}$ of $\sum_{0}^{\infty}\pm\lambda$, where the signs are chosen independently with probability $\frac{1}{2}$. The family $\{\mu_{\lambda}\}$ have been studied since the 1930's. The main question is for which parameters $\lambda$ it holds that $\mu_{\lambda}$ is absolutely continuous. I will describe what is currently known, and present Erdős's argument for the existence of parameters $\frac{1}{2}<\lambda<1$ for which $\mu_{\lambda}$ is singular.

## Date:

Wed, 03/05/2017 - 12:00 to 13:00

רוס 70A