A Relation between the Correlation Dimensions of Multifractal Wavefunctions and Spectral Measures in Integer Quantum Hall Systems
We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets built from states near the metal-insulator transition in the center of the lowest Landau band we find that the return probability to the origin $p(t)$ decays algebraically, $p(t) \sim t^{-D_2/2}$, with a non-conventional exponent $D_2/2$. $D_2$ is the generalized dimension describing the scaling of the second moment of the wavefunction. We show that the corresponding spectral measure is multifractal and that the exponent $D_2/2$ equals the generalized dimension $\widetilde{D}_2$ of the spectral measure.
We model cross-market Bitcoin prices as long-memory processes and study dynamic interdependence in a fractionally cointegrated VAR framework. We find long-memory in both the individual markets and the system of markets depicting non-homogeneous informational inefficiency. Moreover, Bitcoin markets are found to be fractionally cointegrated, where uncertainty negatively impacts this type of cointegration relationship.