We examine the two-point correlation function of local maxima in temperature fluctuations at the last scattering surface when this stochastic field is modified by the additional fluctuations produced by straight cosmic strings via the Kaiser-Stebbins
effect. We demonstrate that one can detect the imprint of cosmic strings with tension $Gmu gtrsim 1.2 times 10^{-8}$ on noiseless $1^prime$ resolution cosmic microwave background (CMB) maps at 95% confidence interval. Including the effects of foregrounds and anticipated systematic errors increases the lower bound to $Gmu gtrsim 9.0times 10^{-8}$ at $2sigma$ confidence level. Smearing by beams of order 4 degrades the bound further to $Gmu gtrsim 1.6 times 10^{-7}$. Our results indicate that two-point statistics are more powerful than 1-point statistics (e.g. number counts) for identifying the non-Gaussianity in the CMB due to straight cosmic strings.
Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned dat
a is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyals coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyals coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyals coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.
We use the multifractal detrended fluctuation analysis (MF-DFA) to study the electrical discharge current fluctuations in plasma and show that it has multifractal properties and behaves as a weak anti-correlated process. Comparison of the MF-DFA resu
lts for the original series with those for the shuffled and surrogate series shows that correlation of the fluctuations is responsible for multifractal nature of the electrical discharge current.
