# On zeros of Martin-Löf random Brownian motion

```@article{Bienvenu2014OnZO,
title={On zeros of Martin-L{\"o}f random Brownian motion},
author={Laurent Bienvenu and Kelty Allen and Theodore A. Slaman},
journal={J. Log. Anal.},
year={2014},
volume={6}
}```
• Published 24 May 2014
• Mathematics, Computer Science
• J. Log. Anal.
We investigate the sample path properties of Martin-Lof random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-Lof random Brownian path, (2) that the effective dimension of zeroes of a Martin-Lof 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-Lof random Brownian path, and (3) we will demonstrate a new proof that the solution to…

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