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סמינר תלמידי מחקר - אריאל רפפורט | Einstein Institute of Mathematics

סמינר תלמידי מחקר - אריאל רפפורט

Date: 
Wed, 03/05/201712:00-13:00
Location: 
רוס 70A
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.