Short-distance wavefunction statistics in one-dimensional Anderson localization

We investigate the short-distance statistics of the local density of states <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\nu$</EquationSource> </InlineEquation> in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$P(\nu)$</EquationSource> </InlineEquation> can be recovered from the long-distance wavefunction statistics, if one also uses parameters that are irrelevant from the perspective of two-parameter scaling theory. Copyright Springer-Verlag Berlin/Heidelberg 2003