Related papers: A generalized plasma and interpolation between cla…
We study the induced spherical ensemble of non-Hermitian matrices with real quaternion entries (considering each quaternion as a $2\times 2$ complex matrix). We define the ensemble by the matrix probability distribution function that is…
We develop a theoretical and computational framework for beam-plasma collective oscillations in intense charged-particle beams at intermediate energies (10-100 MeV). In Part I, we formulate a kinetic field theory governed by the…
We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…
This paper provides bifactor gamma distribution, trivariate gamma distribution and two copula families on [0, 1] n obtained from the Laplace transforms of the multivariate gamma distribution and the multi-factor gamma distribution given by…
We give a closed form for the correlation functions of ensembles of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2 \times 2$ matrix kernel associated to the ensemble. We also derive closed…
We study operators obtained by coupling an $n \times n$ random matrix from one of the Gaussian ensembles to the discrete Laplacian. We find the joint distribution of the eigenvalues and resonances of such operators. This is one of the…
In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional…
We study an ultrarelativistic QED plasma in thermal equilibrium. Plasmons - photon collective excitations - are postulated to correspond not to poles of the retarded photon propagator but to poles of the propagator multiplied by the fine…
The two component plasma (TCP) living in a Flamm's paraboloid is studied at a value of the coupling constant $\Gamma=2$ for which an analytic expression for the grand canonical partition function is available. Two cases are considered, the…
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions.…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
In classical density functional theory (DFT) the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a…
In this paper the kernel for the spectral correlation functions of the invariant chiral random matrix ensembles with real ($\beta =1$) and quaternion real ($\beta = 4$) matrix elements is expressed in terms of the kernel of the…
Using a self-replicating method, we generalize with a free parameter some Borwein algorithms for the number $\pi$. This generalization includes values of the Gamma function like $\Gamma(1/3)$, $\Gamma(1/4)$ and of course…
Analyses of the galaxy N-Point Correlation Functions (NPCFs) have a large number of degrees of freedom, meaning one cannot directly estimate an invertible covariance matrix purely from mock catalogs, as has been the standard approach for…
We find the precise rate at which the empirical measure associated to a $\beta$-ensemble converges to its limiting measure. In our setting the $\beta$-ensemble is a random point process on a compact complex manifolds distributed according…
In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer…
Let $ f_0 $ and $ f_\infty $ be formal power series at the origin and infinity, and $ P_n/Q_n $, with $ \mathrm{deg}(P_n),\mathrm{deg}(Q_n)\leq n $, be a rational function that simultaneously interpolates $ f_0 $ at the origin with order $…
Collective excitations of rotating dusty plasma are analyzed under the quasi localized charge approximation (QLCA) framework for strongly coupled systems by explicitly accounting for the dust rotation in the analysis. Considering the firm…
Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to…