Series: Penn State Logic Seminar

 Date: Tuesday, October 3, 2006

 Time: 2:30 - 3:45 PM

 Place: 106 McAllister Building

 Speaker: Bjorn Kjos-Hanssen, Cornell, Mathematics
 
 Title: Schnorr random paths of Brownian motion

 Abstract:

   Schnorr random paths of Brownian motion are continuous functions
   that satisfy all computable probability laws for Brownian motion
   (in a certain sense).  Similarly, Martin-L"of random paths are
   continuous functions that satisfy all computably enumerable
   probability laws.  The study of these notions goes back to Asarin
   and Pokrovskiy, 1986.

   Fouch'e asked whether for each Martin-L"of random path,
   Khintchine's Law of the Iterated Logarithm holds almost
   everywhere. This was answered in the affirmative by Nerode and
   myself. In fact the result holds for each Schnorr random path. This
   is obtained using the fact that a weak version of van Lambalgen's
   Theorem holds for Schnorr randomness, and using the stationary
   increments of the Brownian motion process.