title: Fluctuations of the inverse participation ratio at the anderson transition
abstract: Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale invariant, with a power-law asymptotic "tail." This scale invariance implies that the fractal dimensions D(q) are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility chi is violated in the regime of strong multifractality, with chi-->1 in the limit D2-->0.
authors.affiliation: Institut fur Theorie der Kondensierten Materie, Universitat Karlsruhe, 76128 Karlsruhe, Germany.
authors.initials: F
authors.lastname: Evers
authors.initials: AD
authors.lastname: Mirlin