The Random Walk 1Dimensional

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=b2IImYrf-pQ

The Random Walk, also knowm as Drunkard's Walk or, with some regards, the discrete Wiener Process, can be used to test the hypothesis if some random variable X has a uniform distribution. Is ilustrated in this video in two stages. In the first stage we retrieve a stream of bits from this source, http://qrng.physik.hu-berlin.de/ a very precise and powerful tool for generating what we know as true random numbers. For each bit we consider de following, if the bit is 1 than the we take a unitary positive step, if the bit is -1 than we take a unitary negative step. As an example supose the following bit stream: • 0,0,1,1,1,1,0 this would result in the folowing points -1,-2,-1,0,1,2,1 and so on. The walk length is the number of bits in the stream. In this ilustration we will be working with walk lengths of size 2000 and performing 4000 walks. This is mainly because in several hypotesis tests its is more appropried to use a larger samples. You will see that in the first 2:30 minutes of the video may be very confusing, but the important thing is that after several walks we observe that the ending points of all walks reach a somewhat fixed upper and lower bound, and most of the walks tend to run inside this bounds. This is somehow important, since that the Drunkard's Walk proposition, states that after some finite number of left(-1), right(1), steps the Drunk will return to its point of origin. As this is a 1-Dimensional ilustration the point of origin is 0 , and the video on it's first stage demonstrates this overall tendency. • The second stage, after around 2:30, we use the same information used on the first stage, with the same proposition bit 0 step -1 bit 1 step 1, howeve we wont sum de steps we will sum each walk. As an example let's take 2 bit sequences: • Bits Steps • 1,0,1,0,1,0,1,0 | 1,-1,1,-1, 1,-1,1,-1 • 1,1,1,1,0,0,1,1 | 1, 1,1, 1,-1,-1,1,1 • if we sum the steps we obtain the following sequence. • Sum = 2,0,2,0,0,-2,2,0 • This process follows for all the 4000 walks of size 2000. It must be observed that after several steps the curve iteratively being plotted looks much alike with withe noise another way of observe if some set of data is actualy random. • My name is Fernando Ducha, [email protected], this is part of a project being done for the Centro Federal de Edecucação Tecnológica of Minas Gerais - Brazil. The software developed to produce this vídeo is based much on teachings of Prof. Allbens Atman Picardi Faria, although any error or misguided concept in this work can't be attributed to him. • Following Work: • We expect to present an allometric curve fitting to this data. And provide more data, that can ilustrate the means of randomness testing. But if you are realy interested take a look at, Art of Computer Programming, Volume 2: Seminumerical Algorithms from Donald E. Knuth, it's dense, mathematicaly deep, but is a must to know to book. Section 3.3, presents several tests, and none of them is a Reader's Digest Literature. • To any of you who have watched it, plz post your comments and criticize as mush as you can. There is no absolute truth and nobody is beyond the threshold of being wrong.

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