With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...

Non-Gaussian velocity distribution in star forming region is reproduced by inelastic clump collision model. We numerically calculated the evolution of inelastic hard spheres in sheared flow, which corresponds to cloud clumps in differential galactic rotation. This system fluctuates largely around equilibrium state, creating clusters with inelastic collisions and destroying them with shear motio...

Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability distribution is Gaussian. On the other hand, in the fluidized phase, where the particles can exchange their positions, the distribution clearly deviates from Ga...

The number of levels with energy less than E of an integrable quantum system with two degrees of freedom is equal to XE+sE', where A, is a constant and s a Auctuating quantity with a non-Gaussian distribution. The probability distribution of s decreases roughly like exp( —s ) when s is large. The number of levels between E and E+zJE is equal to kz JE+rE 'I where r is another lluctuating quantit...

Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability distribution is Gaussian. On the other hand, in the uidized phase, where the particles can exchange their positions, the distribution clearly deviates from Gaus...

We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution serves as mapping between the three ensembles. The statistics of the wireless fading amplitude, as modeled by Nakagami-m distribution, provide a rare example o...

Warning: notes are incomplete and unchecked for correctness 1 Gaussian distribution 1.1 Definition The (standard) Gaussian distribution on the real line R is defined by its density function φ(z) := 1 √ 2π exp(−z 2 /2). The notation Z ∼ N (0, 1) means that the real-valued random variable Z follows the standard Gaussian distribution. The " N " probably comes from the fact that the distribution is...

With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...

We find the limit distributions for a spectrum of a system of n particles governed by a k–body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q–deformed Gaussian distribution with the deformation parameter q depending on the value of the fraction k √ n . The family of q–deformed Gaussian distributions include the Gau...

We find the limit distributions for a spectrum of a system of n particles governed by a k–body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q–deformed Gaussian distribution with the deformation parameter q depending on the value of the fraction k √ n . The family of q–deformed Gaussian distributions include the Gau...