Fouché, Willem Louw and Mukeru, Safari and Davie, George - Fourier spectra of measures associated with algorithmically random Brownian motion

lmcs:819 - Logical Methods in Computer Science, September 12, 2014, Volume 10, Issue 3
Fourier spectra of measures associated with algorithmically random Brownian motion

Authors: Fouché, Willem Louw and Mukeru, Safari and Davie, George

In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion. We show that, under some computability conditions on these sets, the Fourier transform of the associated measures have, relative to the Hausdorff dimensions of these sets, optimal asymptotic decay at infinity. The argument relies heavily on a direct characterisation, due to Asarin and Pokrovskii, of algorithmically random Brownian motion in terms of the prefix free Kolmogorov complexity of finite binary sequences. The study also necessitates a closer look at the potential theory over fractals from a computable point of view.


Source : oai:arXiv.org:1406.3715
DOI : 10.2168/LMCS-10(3:20)2014
Volume: Volume 10, Issue 3
Published on: September 12, 2014
Submitted on: June 25, 2015
Keywords: Computer Science - Computational Complexity


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