On zeros of Martin-L\"of random Brownian motion
Logic
2014-06-09 v3
Abstract
We investigate the sample path properties of Martin-L\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\"of random Brownian path, (2) that the effective dimension of zeroes of a Martin-L\"of 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-L\"of random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable.
Keywords
Cite
@article{arxiv.1405.6312,
title = {On zeros of Martin-L\"of random Brownian motion},
author = {Kelty Allen and Laurent Bienvenu and Theodore Slaman},
journal= {arXiv preprint arXiv:1405.6312},
year = {2014}
}