2014/09/03 by Willem L. Fouché, Willem L. Fouche, Fouche, Willem L.
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Mathematical Dynamics and Fractals #cs.LO
paper · pdf · doi:10.48550/arxiv.1409.1752
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
arxiv created 2014/09/03 · openalex publication_date 2014/09/03 · arxiv updated 2014/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-Löf 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.