Jonathan Fraser

Title:  Fourier decay of measures on the Brownian graph 


Abstract: Roughly speaking, a set is ?Aarries a measure whose 
          Fourier transform decays like x s/2 where s is the Hausdorff 
          dimension of the set (this is the fastest possible decay). 
          Salem sets are often found via random processes, such as the 
          image or level sets of a random function; like Brownian motion, 
          for example.  /Kahane asked in 1993 whether or not the graph of 
          the classical Brownian motion is almost surely a Salem set. In
          this talk I will discuss this problem: first I will show that the
          answer is no, it is not almost surely a Salem set, and secondly I
          I will give the optimal almost surely rate of Fourier decay for
          measures on the Brownian graph (which is less than s/2). The 
          First part of the talk is joint work with Tuomas Orphonen
          (University of Helsinki) and Tuomas Sahlsten (University of Bristol)
          and the second part is joint with Tuomas Sahlsten.