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arXiv · 1405.6312

On zeros of Martin-Löf random Brownian motion

Kelty Allen·Laurent Bienvenu·Theodore Slaman
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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.

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Kelty Allen, Laurent Bienvenu, Theodore Slaman. 2014-06-06. On zeros of Martin-Löf random Brownian motion. https://arxiv.org/abs/1405.6312

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