Robin Deeley (CU Boulder) Wieler solenoids and the K-theory of the associated stable and stable Ruelle algebras
! CANCELED ! Thu, Nov. 14
Probability
Dan Stroock (MIT) Some Applications of Gaussian Measures
X
Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Through examples I will discuss how this allows one to compute the K-theory of the stable algebra, S, and the stable Ruelle algebra, S\rtimes Z. These computations involve writing S as a stationary inductive limit and S\rtimes Z as a Cuntz-Pimsner algebra.
X
Suppose $X$ and $Y$ are independent, identically distributed real valued random variables and that $\theta \in (0,1)$. Then $\theta \phantom{\rule{0}{0ex}}X+\sqrt{1-{\theta}^{2}}Y$ has the same distribution as $X$ and $Y$ if and only if these are centered Gaussian random variables. Equivalently, if $\mu$ is a Borel probability measure on $\mathbb{R}$, then $\hat{\mu}(\xi )=\hat{\mu}(\theta \phantom{\rule{0}{0ex}}\xi )\hat{\mu}(\sqrt{1-{\theta}^{2}}\xi )$ if and only if $\mu$ is a centered Gaussian measure.
In this lecture I will first prove this result in the case when $\theta ={2}^{-1/2}$ and then give some applications of it.