Related papers: Free Convolution and Generalized Dyson Brownian Mo…
In the past 20 years, the study of real eigenvalues of non-symmetric real random matrices has seen important progress. Notwithstanding, central questions still remain open, such as the characterization of their asymptotic statistics and the…
The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf)…
The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…
Dyson's Brownian motion model with the parameter $\beta=2$, which we simply call the Dyson model in the present paper, is realized as an $h$-transform of the absorbing Brownian motion in a Weyl chamber of type A. Depending on initial…
In order to obtain stable and accurate general relativistic simulations, re-formulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…
Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary…
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
Open systems acquire time-dependent coupling constants through interaction with an external field or environment. We generalize the Lewis-Riesenfeld invariant theorem to open system of quantum fields after second quantization. The…
A new approach to the generalised Brownian motion introduced by M. Bozejko and R. Speicher is described, based on symmetry rather than deformation. The symmetrisation principle is provided by Joyal's notions of tensorial and combinatorial…
The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare…
It is shown that the correlation functions of the random variables $\det(\lambda - X)$, in which $X$ is a real symmetric $ N\times N$ random matrix, exhibit universal local statistics in the large $N$ limit. The derivation relies on an…
A new type of Coulomb gas is defined, consisting of arbitrary numbers of point charges of two species executing Brownian motions under the influence of their mutual electrostatic repulsion. Being a generalization of a model of identical…
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…
A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…
It is well known that freeness appears in the high-dimensional limit of independence for matrices. Thus, for instance, the additive free Brownian motion can be seen as the limit of the Brownian motion on hermitian matrices. More generally,…