Wavelets and multifractality: Application to Anderson localized wave functions

We discuss a simple method for analysing the local scaling behavior of the fluctuations of random probability distributions. The usefulness of the method, based on a discrete wavelet approach, is illustrated for the case of Anderson localized wave functions, $\psi(x)$, in one dimension, for which the standard multifractal analysis has led to controversial conclusions. The method suggests that $\vert\psi(x)\vert^2$ is not multifractal in space and has similar statistical properties as profiles generated by simple random walks in one dimension