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Diophantine properties of Brownian motion: recursive aspects (1409.1752v1)
Published 3 Sep 2014 in cs.LO
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.