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We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number…

High Energy Physics - Theory · Physics 2009-10-28 J. J. M. Verbaarschot , I. Zahed

It is argued that the short time scale phenomena can be studied within the framework of hydrodynamics in the quark-gluon plasma. There are two different versions of the hydrodynamic-like equations in the literature. In this work we discuss…

High Energy Physics - Phenomenology · Physics 2011-05-12 Abhishek Basak , Jitesh R. Bhatt , Predhiman K. Kaw

We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…

Mathematical Physics · Physics 2011-12-06 A. Abd El-Hady , A. Y. Abul-Magd

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

Disordered Systems and Neural Networks · Physics 2025-01-30 Joseph W. Baron , Thomas Jun Jewell , Christopher Ryder , Tobias Galla

I begin by discussing the basic ideas of quantum field theory (QFT). I provide a review of symmetries in physics and then move on to discuss the quark model. I then review lattice gauge theory with particular attention paid to lattice QCD…

High Energy Physics - Lattice · Physics 2009-09-29 W Armour

We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystr\"om-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of…

High Energy Physics - Lattice · Physics 2019-09-04 Hiroyuki Fuji , Issaku Kanamori , Shinsuke M. Nishigaki

We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process…

Probability · Mathematics 2018-08-07 Reda Chhaibi , Joseph Najnudel , Ashkan Nikeghbali

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-colour lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues…

High Energy Physics - Lattice · Physics 2009-11-11 G. Akemann , E. Bittner

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…

Statistical Mechanics · Physics 2013-05-29 Carsten Timm

We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real nonvanishing eigenvalues, as well as $M-N$ zero…

Condensed Matter · Physics 2009-10-28 Joshua Feinberg , A. Zee

Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…

Statistical Mechanics · Physics 2026-04-27 Abbas Ali Saberi , Roderich Moessner

We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices…

chao-dyn · Physics 2009-10-31 Karol Zyczkowski , Hans-Juergen Sommers

We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…

chao-dyn · Physics 2008-02-03 Henrik J. Pedersen , A. D. Jackson

In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…

Statistical Mechanics · Physics 2008-02-03 M. Caselle

Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…

Mathematical Physics · Physics 2015-09-17 Eva-Maria Graefe , Steve Mudute-Ndumbe , Matthew Taylor

The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…

High Energy Physics - Lattice · Physics 2015-06-25 Robert G. Edwards , Urs M. Heller , Joe Kiskis , Rajamani Narayanan

We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well…

Probability · Mathematics 2015-10-05 Christian Webb

There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…

Chaotic Dynamics · Physics 2007-05-23 V. K. B. Kota , R. Sahu

We compute statistical distributions of individual low-lying eigenvalues of random matrix ensembles interpolating chiral Gaussian symplectic and unitary ensembles. To this aim we use the Nystrom-type discretization of Fredholm Pfaffians and…

High Energy Physics - Lattice · Physics 2015-04-02 Shinsuke M. Nishigaki , Takuya Yamamoto

The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy $E_c\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger…

High Energy Physics - Lattice · Physics 2015-06-25 M. E. Berbenni-Bitsch , M. Göckeler , H. Hehl , S. Meyer , P. E. L. Rakow , A. Schäfer , T. Wettig