Complexity Explorer Santa Fe Institute

Random Walks

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2.1 Root Mean Square Displacement » Quiz solutions

2.1 Q1 

For the Pearson random walk in which the average length of a single step
equals one, what the the root mean square (rms) displacement after 10 steps?

\left | \vec{x_{i}} \right |=a=1

X_{rms}\left ( N=10 \right )= ?

X_{rms}=\sqrt{\left \langle \vec{x}^{2}_{N} \right \rangle} = \sqrt{N}\cdot a = \sqrt{10}\cdot 1 = 3.16

 

2.1 Q2 

For this Pearson random walk, what is the rms displacement after 1000000
steps?

X_{rms}\left ( N=10^{6} \right )= ?

X_{rms}=\sqrt{\left \langle \vec{x}^{2}_{N} \right \rangle} = \sqrt{N}\cdot a = \sqrt{10^{6}}\cdot 1 = 10^{3}