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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Kolmogorov complexity and Fourier aspects of Brown
ian motion - Fouche\, W (University of South Afric
a)
DTSTART;TZID=Europe/London:20120705T140000
DTEND;TZID=Europe/London:20120705T143000
UID:TALK38870AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/38870
DESCRIPTION:It is well-known that the notion of randomness\, s
uitably refined\, goes a long way in dealing with
the tension between the ``incompatability of short
est descriptions and of effecting the most-economi
cal algorithmical processing" Manin(2006). In this
work\, we continue to explore this interplay betw
een short descriptions and randomness in the conte
xt of Brownian motion and its associated geometry.
In this way one sees how random phenomena associa
ted with the geometry of Brownian motion\, are imp
licitly enfolded in each real number which is comp
lex in the sense of Kolmogorov. These random pheno
mena range from fractal geometry\, Fourier analysi
s and non-classical noises in quantum physics. In
this talk we shall discuss countable dense random
sets as the appear in the theory of Brownian motio
n in the context of algorithmic randomness. We sha
ll also discuss applications to Fourier analysis.
In particular\, we also discuss the images of cert
ain $Pi_2^0$ perfect sets of Hausdorff dimension z
ero under a complex oscillation (which is also kno
wn as an algorithmically random Brownian motion).
This opens the way to relate certain non-classical
noises to Kolmogorov complexity. For example\, th
e work of the present work enables one to represen
t Warren's splitting noise directly in terms of in
finite binary strings which are Kolmogorov-Chaitin
-Martin-Lö\;f random.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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