Date: Apr 3, 2013 3:17 AM
Author: David Bernier
Subject: Brownian motion sample path: fake or genuine?
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:

http://img203.imageshack.us/img203/9220/brown1.png

Maybe it's a fake, not random.

I don't know ...

David Bernier

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