Power-law random walks

Details Power-law random walks Power-law random walks

2006-06-29

arxiv.org/abs/cond-mat/0606768v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

10.1103/PhysRevE.74.051124

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.

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