# What are the differences between the random walk and the gaussian random walk?

I know the random walk mobility model, but I can not understand what are the differences with respect to gaussian random walk.

In other words, I know how to implement the two-dimensional random walk: in according to the random walk mobility model, each node moves with a speed and direction choosen at random using the following rules:

1. the speed $v$ is uniformly chosen in the range $[V_{min}, V_{max}]$.
2. the direction $\theta$ is uniformly chosen in the range $[0, 2\pi]$.
3. moreover also a time interval $\Delta t$ is uniformly chosen in the range $[T_{min}, T_{max}]$: given the speed and the time interval, the distance of the trip is $d= (v)(\Delta t)$, so it is also possible to calculate the destination $(x, y)$ of the trip.

However, since I do not understand the differences with respect to gaussian random walk, I can not understand how to implement two-dimensional gaussian random walk.

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## 1 Answer

In dimension $1$, the position $X_n$ of a random walk after $n$ steps is $X_n=\sum\limits_{k=1}^nY_k$ where the random variables $(Y_k)_{k\geqslant1}$ are i.i.d. and the distribution of each $Y_k$ is Bernoulli, that is, $Y_k=\pm1$. The position $X^G_n$ of a gaussian random walk after $n$ steps is $X^G_n=\sum\limits_{k=1}^nY^G_k$ where the random variables $(Y^G_k)_{k\geqslant1}$ are i.i.d. and the distribution of each $Y^G_k$ is normal.

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How does it work in two dimensions? Would perhaps be $X_n$ a vector with two elements? – enzom83 Oct 30 '12 at 13:19