Multifractality at the spin quantum Hall transition

Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $\Delta_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$.Comment: 4 pages, 3 figure

New Results on the Cucconi Test

This paper is focused on the test of Cucconi (1968), a rank test for the for the location-scale problem. The test is of interest because, contrary to the other location-scale tests, it is not a quadratic form of a test on location and a test on scale, and it is based on squared ranks and squared counter-ranks. The power of the Cucconi test has been studied. Simulations show that the test of Cucconi maintains the size very close to Ą and is more powerful than the well-known Lepage test, and therefore should be taken into account as a better alternative when it is not possible to develop an efficiency robust procedure for the problem at hand