Zobrazeno 1 - 10
of 56
pro vyhledávání: '"FOUCHÉ, WILLEM"'
Autor:
Fouche, Willem, Mukeru, Safari
In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path which is Martin-L\"of random with respect to the Wiener measure has con
Externí odkaz:
http://arxiv.org/abs/2208.01877
Autor:
Fouché, Willem L., Mukeru, Safari
Publikováno v:
In Theoretical Computer Science 10 November 2023 979
Autor:
Fouché, Willem, Lee, Hyunwoo, Lim, Donghyun, Park, Sewon, Schröder, Matthias, Ziegler, Martin
We consider randomized computation of continuous data in the sense of Computable Analysis. Our first contribution formally confirms that it is no loss of generality to take as sample space the Cantor space of infinite FAIR coin flips. This extends [S
Externí odkaz:
http://arxiv.org/abs/1906.06684
Publikováno v:
Logical Methods in Computer Science, Volume 14, Issue 2 (May 22, 2018) lmcs:3245
We introduce the notion of being Weihrauch-complete for layerwise computability and provide several natural examples related to complex oscillations, the law of the iterated logarithm and Birkhoff's theorem. We also consider hitting time operators, w
Externí odkaz:
http://arxiv.org/abs/1505.02091
Autor:
Pauly, Arno, Fouché, Willem L.
Given some set, how hard is it to construct a measure supported by it? We classify some variations of this task in the Weihrauch lattice. Particular attention is paid to Frostman measures on sets with positive Hausdorff dimension. As a side result, t
Externí odkaz:
http://arxiv.org/abs/1409.3428
Autor:
Fouche, Willem L.
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 o
Externí odkaz:
http://arxiv.org/abs/1409.1752
Autor:
Fouche, Willem L.
Publikováno v:
Math. Struct. Comp. Sci. 25 (2015) 1590-1606
In this paper, we continue the study of the geometry of Brownian motions which are encoded by Kolmogorov-Chaitin random reals (complex oscillations). We unfold Kolmogorov-Chaitin complexity in the context of Brownian motion and specifically to phenom
Externí odkaz:
http://arxiv.org/abs/1409.1060
Publikováno v:
Logical Methods in Computer Science, Volume 10, Issue 3 (September 12, 2014) lmcs:819
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
Externí odkaz:
http://arxiv.org/abs/1406.3715
Autor:
Fouché, Willem L.
We study, in the context of algorithmic randomness, the closed amenable subgroups of the symmetric group $S_\infty$ of a countable set. In this paper we address this problem by investigating a link between the symmetries associated with Ramsey Fra\"i
Externí odkaz:
http://arxiv.org/abs/1308.5506
Autor:
Fouche, Willem L.
We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fra\" {i}ss\' e limits) to study closed amenable subgroups $G$ of the symmetric group $S_\infty$ of a countable set, where $S_\infty$ has
Externí odkaz:
http://arxiv.org/abs/1205.0386