2014/05/24 by Kelty Allen, Allen, Kelty, Laurent Bienvenu +3
Mathematics · #03D32 #03F60 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03D32 #msc:03F60
paper · pdf · doi:10.48550/arxiv.1405.6312
arxiv created 2014/06/06 · arxiv updated 2014/06/09
We investigate the sample path properties of Martin-Löf random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-Löf random Brownian path, (2) that the effective dimension of zeroes of a Martin-Löf random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero of some Martin-Löf random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable.