文章基本信息

标题：Fourier spectra of measures associated with algorithmically random Brownian motion
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作者：Willem Fouche' ; Safari Mukeru ; George Davie 等
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2014
卷号：10
期号：3
页码：1
DOI：10.2168/LMCS-10(3:20)2014
出版社：Technical University of Braunschweig
摘要：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.
其他关键词：Kolmogorov complexity, algorithmic randomness, Brownian motion, Hausdorff dimension, Fourier dimension, Salem sets.