On zeros of MartinLöf random Brownian motion
Abstract
We investigate the sample path properties of MartinLöf random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every MartinLöf random Brownian path, (2) that the effective dimension of zeroes of a MartinLöf 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 MartinLöf random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.6312
 Bibcode:
 2014arXiv1405.6312A
 Keywords:

 Mathematics  Logic;
 03D32;
 03F60