On zeros of Martin-Löf random Brownian motion
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2014
- arXiv:
- arXiv:1405.6312
- Bibcode:
- 2014arXiv1405.6312A
- Keywords:
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- Mathematics - Logic;
- 03D32;
- 03F60