Fall 2014, Thursdays, Blocker 506A, 4:00-4:50 PM

Date: October 23

"  Limit theorems for composition of functions "
  Prof. Michael Anshelevich  


Let F be an analytic function mapping the upper half of the complex plane to itself. We will consider the behavior of such functions under composition. Here are some questions we will discuss. Does such a function have a square root under composition? Can it be included in a continuous composition semigroup? Under what conditions will n-fold compositions of such functions (which are themselves approaching the identity function), approach a limit? And what does any of this have to do with probability theory?