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.