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arXiv · 1409.1752

Diophantine properties of Brownian motion: recursive aspects

Willem L. Fouche
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Abstract

We use recent results on the Fourier analysis of the zero sets of Brownian motion to explore the diophantine properties of an algorithmically random Brownian motion (also known as a complex oscillation). We discuss the construction and definability of perfect sets which are linearly independent over the rationals directly from Martin-L\"of random reals. Finally we explore the recent work of Tsirelson on countable dense sets to study the diophantine properties of local minimisers of Brownian motion.

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Willem L. Fouche. 2014-09-03. Diophantine properties of Brownian motion: recursive aspects. https://arxiv.org/abs/1409.1752

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