This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are also given on real data, both new data sets and well-studied data sets. All data and tools used are freely available for download along with simple “recipes” wh...

A one-dimensional tight-binding Hamiltonian describes the evolution of a single impurity interacting locally with N electrons. The impurity spectral function has a power-law singularity A(ω) ∝| ω− ω0 |−1+β with the same exponent β that characterizes the logarithmic decay of the quasiparticle weight Z with the number of electrons N , Z ∝ N−β. The exponent β is computed by (1) perturbation theory...

We study the asymptotic expansions with respect to h of

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent α ≈ 1.1 for intermediate and with exponent γ ≈ 0.6 for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a ...

We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: D t u(t, x) = Bu + u · Ẇ , where D t is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R and Ẇ a time homogeneous fractional ...

We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step reduce the sparseness of original problem with recursive Green’s function method. apply this framework investigate critical behavior integer quantum Hall transition Hamiltonian defined simple square lattice. In addition, we employ imp...

We consider the role of finite size effects on the value of the effective Hurst exponent H . This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer’s identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = 1/2) i...

An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent alpha(min) that characterizes the "hottest" region of the harmonic measure and the fractal dimension D of the cluster, i.e., D=1+alpha(min). Due to lack of accurate direct measurements of both D and alpha(min), this conjecture ...

The results of kinetic Monte Carlo simulations of epitaxial growth on fcc~100! and bcc~100! surfaces in which the correct crystal geometry is taken into account are reported. The existence of downward funneling to fourfold hollow sites leads to a downward current for large angles and to angle selection as observed in a variety of experiments. We have used our model to simulate Fe/Fe~100! deposi...