Diophantine properties of Brownian motion: recursive aspects
Logic in Computer Science
2014-09-08 v1
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.
Keywords
Cite
@article{arxiv.1409.1752,
title = {Diophantine properties of Brownian motion: recursive aspects},
author = {Willem L. Fouche},
journal= {arXiv preprint arXiv:1409.1752},
year = {2014}
}
Comments
Appeared in: Logic, Computation, Hierarchies, (Brattka, Diener, Spreen (Eds)), Ontos Verlag, 2014, pp 139-156. arXiv admin note: substantial text overlap with arXiv:1409.1060