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We study the spectrum of the hermitian Wilson Dirac operator in the epsilon-regime of QCD in the quenched approximation and compare it to predictions from Wilson Random Matrix Theory. Using the distributions of single eigenvalues in the…

High Energy Physics - Lattice · Physics 2011-12-22 Albert Deuzeman , Urs Wenger , Jaïr Wuilloud

We re-analyze data from available finite-temperature QCD simulations near the chiral transition, with the help of Chiral Random Matrix Theory (chRMT). Statistical properties of the lowest-lying eigenvalues of the staggered Dirac operator…

High Energy Physics - Lattice · Physics 2009-10-31 F. Farchioni , Ph. de Forcrand , I. Hip , C. B. Lang , K. Splittorff

In this paper, we study the classification problem by estimating the conditional probability function of the given data. Different from the traditional expected risk estimation theory on empirical data, we calculate the probability via…

Machine Learning · Computer Science 2022-10-14 Meng-Xian Zhu , Yuan-Hai Shao

In this lecture we discuss correlations of the QCD Dirac eigenvalues. We find that below a scale of $E_c\sim \Lambda/L^2$ they are given by chiral Random Matrix Theory. This follows from analytical arguments based on partially quenched…

High Energy Physics - Theory · Physics 2007-05-23 J. J. M. Verbaarschot

The reasons for using low-lying Dirac eigenmodes to probe the local structure of topological charge fluctuations in QCD are discussed, and it is pointed out that the qualitative double-peaked behavior of the local chiral orientation…

High Energy Physics - Lattice · Physics 2008-11-26 I. Horvath , S. J. Dong , T. Draper , N. Isgur , F. X. Lee , K. F. Liu , J. McCune , H. B. Thacker , J. B. Zhang

In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…

Statistical Mechanics · Physics 2011-08-08 Ivana Vidanovic , Aleksandar Bogojevic , Antun Balaz , Aleksandar Belic

We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…

Data Structures and Algorithms · Computer Science 2017-03-07 Ilias Diakonikolas , Daniel M. Kane , Vladimir Nikishkin

An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…

Astrophysics · Physics 2012-12-12 Burkhard Zink

We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…

Probability · Mathematics 2011-08-16 Ioana Dumitriu

In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…

Probability · Mathematics 2021-03-23 Jianfeng Yao , Wangjun Yuan

In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…

Methodology · Statistics 2021-10-22 Bhupendra Singh , Varun Agiwal , Ravindra Pratap Singh , Abhishek Tyagi

In this work we probe the QCD Anderson transition by studying spectral distributions of the massless overlap operator on gauge configurations created by the twisted mass at finite temperature collaboration (tmfT) with 2+1+1 flavors of…

High Energy Physics - Lattice · Physics 2024-04-30 Robin Kehr , Dominik Smith , Lorenz von Smekal

Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study…

Mathematical Physics · Physics 2013-11-13 Marek Smaczynski , Tomasz Tkocz , Marek Kus , Karol Zyczkowski

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We use a random matrix model approach to calculate analytically all correlation functions at weak and strong non-Hermiticity for…

High Energy Physics - Lattice · Physics 2007-05-23 G. Akemann

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory…

High Energy Physics - Lattice · Physics 2008-11-26 Elmar Bittner , Simon Hands , Harald Markum , Rainer Pullirsch

We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…

Spectral Theory · Mathematics 2013-11-27 Jean-Claude Cuenin

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory…

High Energy Physics - Lattice · Physics 2009-10-31 H. Markum , R. Pullirsch , K. Rabitsch , T. Wettig

We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-$\frac{1}{2}$ particle incident upon a rectangular barrier. Using the transfer matrix…

Disordered Systems and Neural Networks · Physics 2020-03-10 Abhay Mehta , Sandeep Joshi , Sudhir R. Jain

In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. The limiting distribution is well described by its moments. Here, an analytical approach allows us, as in the case of Wigner…

Probability · Mathematics 2025-12-04 Lucas Babet , Ionel Popescu

We present a study of the Dirac eigenvalue spectrum near the region of the QCD phase transition. This study makes use of a sequence of ensembles with temperatures from 150 MeV to 200 MeV generated with $2 + 1$ flavors of dynamical domain…

High Energy Physics - Lattice · Physics 2011-11-07 Zhongjie Lin