Narrow Results

In this paper, we prove strong convergence of $q$-Gaussians with respect to a parameter $q$, which implies the spectrum of any self-adjoint non-commutative polynomial in $q$-Gaussians is continuously deformed with respect to $q$. With Bożejko’s Haagerup-type inequality, we follow Brannan’s approach to proving the asymptotic strong convergence of the free orthogonal quantum group.

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.

The stability of the time base of an oscilloscope has been analyzed by digitizing sinusoidal signals from precision sinusoidal voltage generators. Frequency domain analysis of the recorded data has been performed using the Fourier transform routine built into the recording device, after suitable windowing. Due to the stability of the frequency of the used signals, the expected frequency spectra would be Gaussian functions due to any uncorrelated noise born in all devices connecting the voltage signal generator to the memories of the oscilloscope. The experimental power spectra present instead a non-Gaussian shape, mainly in the points far from their mean values, showing raised "skirt", which a pure Gaussian function is clearly unable to fit. Among the many "deformed" Gaussian distribution functions, those named q-Gaussian and κ-Gaussian respectively, from the symbols used for the characterizing parameters, are instead in good agreement with all experimental power spectra. These results can be attributed mainly to correlated drifts in the time base of the oscilloscope.