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The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…
We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from…
Atmospheric turbulence degrades the performance of free-space optical (FSO) communication and remote sensing systems by introducing phase and intensity distortions. While a majority of research focuses on mitigating these effects to ensure…
First, we make a revision of the up-to-date Passive Scalar Fields properties: also, the refractive index is among them. Afterwards, we formulated the properties that make the family of `isotropic' fractional Brownian motion (with parameter…
Probabilistic forecasts of wind speed are important for a wide range of applications, ranging from operational decision making in connection with wind power generation to storm warnings, ship routing and aviation. We present a statistical…
Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of…
Localization properties of residue fluctuations in globular proteins are studied theoretically by using the Gaussian network model. Participation ratio for each residue fluctuation mode is calculated. It is found that the relationship…
Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…
Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: weakness of collisional dissipation and…
In power system operation, characterizing the stochastic nature of wind power is an important albeit challenging issue. It is well known that distributions of wind power forecast errors often exhibit significant variability with respect to…
We use the theory of Bernstein functions, completely monotonic functions, and Levy processes to define a positive random process $\tau(t)$. For radar clutter one may think of $\tau(t)$ as the instantaneous power of the scattered radar…
This work presents a new theoretical and numerical model describing all possible linear interactions between upper-hybrid wave turbulence and random density fluctuations in a solar wind plasma; not only linear processes as wave reflection,…
The Parker Solar Probe mission provides a unique opportunity to characterize several features of the solar wind at different heliocentric distances. Recent findings have shown a transition in the inertial range spectral and scaling…
The Random Phase and Amplitude Formalism (RPA) has significantly extended the scope of weak turbulence studies. Because RPA does not assume any proximity to the Gaussianity in the wavenumber space, it can predict, for example, how the…
Measurements have been made of the probability distribution of total transmission of microwave radiation in waveguides filled with randomly positioned scatterers which would have values of the dimensionless conductance g near unity. The…
We present experimental results on simultaneous space-time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as…
We review recent results on the appearance of long-term persistence in climatic records and their relevance for the evaluation of global climate models and rare events.The persistence can be characterized, for example, by the correlation…
The Matern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set…
Using the international ground-based network of two-frequency receivers of the GPS navigation system provides a means of carrying out a global, continuous and fully-computerized monitoring of phase fluctuations of signals from…