Analysis and Probability Theory Seminar

It is a classical result that mixing properties of Gaussian processes can be discerned through their associated spectral measure. It turns out that a similar phenomenon holds true for α-stable processes. In this talk, I will introduce the spectral representation of α-stable processes and discuss recent results on how it reflects their mixing properties. In contrast to Gaussian processes, in which the spectral measure is available when the indexing group is Abelian, our results in α-stable processes hold to the generality of all amenable groups.