Exchangeable pairs for weak convergence and a.s. convergence on chaoses (Guangqu Zheng - Kansas University)

Abstract: This talk consists of two parts: the first part is about recent advances on fourth moment phenomena via exchangeable pairs, and will be a quick overview. The second part of the talk will be the main focus of this talk, and will provide several new phenomena concerning a.s. convergence of homogeneous chaoses that include Gaussian Wiener chaoses and homogeneous sums in centered independent random variables. The second part is based on a recent work with Guillaume Poly.