We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of nite approximants, we nd that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble, and thus diiers from the critical level-spacing distribution observed at the metal...

We show that the random matrix theory with non-integer " symmetry parameter " β describes the statistics of transport parameters of strongly disordered two dimensional systems. The application of the random matrix theory (RMT) [1] to electronic transport in weakly disordered systems [2] enables us to understand the main features of the transport. The small number of parameters which enters RMT ...

The first part of this paper surveys generating functions methods in the study of random matrices over finite fields, explaining how they arose from theoretical need. Then we describe a probabilistic picture of conjugacy classes of the finite classical groups. Connections are made with symmetric function theory, Markov chains, Rogers-Ramanujan type identities, potential theory, and various meas...

3 Abstract In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively deenite random hermitean matrices is established. This relationship enables one to present several more or less closed expressions for the oscillator energy. One of such expressions is given in t...

We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these identities arise from combinatorial interpretations of certain properties of the β-Hermite and β-Laguerre ensembles of random matrix theory. We conclude by p...

Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: i) starting from the low-energy effective Lagrangian and ii) starting from a random matrix theory with the symmetries of the Dirac operator. This suggests that the effective theory can be obtained directly from the random matrix theory. Previously, this was shown for thr...

Introduction. A random matrix in a linear system model [1]. Basic examples (involving a single random matrix): CDMA [2], Single-User MIMO [3], compressive sensing [4, 5]. More involved examples (involving sum and products of random matrices): multi-cell communication [6], correlated systems [7], Multiple Access Channels, relay channels [8]. Short discussion on modeling of wireless networks with...

The connection between random matrix theory and the Riemann zeta function was established in 1973 when Montgomery, who had conjectured the 2-point correlations of the Riemann zeros, and Dyson, who was interested in similar statistics of the eigenvalues of ensembles of unitary matrices, realized that the formulae they had discovered independently were in fact identical in a natural asymptotic li...

We consider QCD3 with an odd number of flavors in the mesoscopic scaling region where the field theory finite-volume partition function is equivalent to a random matrix theory partition function. We argue that the theory is parity invariant at the classical level if an odd number of masses are zero. By introducing so-called pseudo-orthogonal polynomials we are able to relate the kernel to the k...

Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural netw...