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Topic: Brownian motion sample path: fake or genuine?
Replies: 7   Last Post: Apr 3, 2013 8:12 PM

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David Bernier

Posts: 3,892
Registered: 12/13/04
Brownian motion sample path: fake or genuine?
Posted: Apr 3, 2013 3:17 AM
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I used snow (white noise) from an analog cathode ray tube TV,
recorded with a webcam, as the source of entropy for supposedly
random bits.

I had 1.8 gigabytes of digital video, which I
whittled down to about 2.5 megabytes of "random bits".

16384 Bernoulli(1205, 1/2) r.v.s were generated,
with k in {0, ... 1205} associated
to the #0 s minus #1s : 2k-1205 in
the range {-1205, -1203, ... -1, 1, 3, 5, ... 1203, 1205}.
This number, 2k-1205, stood in for a Gaussian r.v. of
mean zero. The result was a random walk with steps
of +1 and -1, sampled every 1205 steps;
16384 samples were taken, without counting
x(0) = 0 [starting point].

16384*1205 = 19,742,720 (bits) or 2,467,840 bytes.

The graphic drawn with MatLab is here:

Maybe it's a fake, not random.
I don't know ...

David Bernier


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