相关论文: Spacing distributions in random matrix ensembles

Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation…

In this paper we review and compare the numerical evaluation of those probability distributions in random matrix theory that are analytically represented in terms of Painlev\'e transcendents or Fredholm determinants. Concrete examples for…

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between…

We consider the universality of the nearest neighbour eigenvalue spacing distribution in invariant random matrix ensembles. Focussing on orthogonal and symplectic invariant ensembles, we show that the empirical spacing distribution…

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…

This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…

Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…

In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…

The scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles is evaluated in terms of a Painlev\'e V transcendent. This same Painlev\'e V transcendent is known from the work of Tracy and Widom,…

This is an expository account of the edge eigenvalue distributions in random matrix theory and their application in multivariate statistics. The emphasis is on the Painlev\'e representations of these distributions.

We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real…

This paper is concerned with certain connections between the ensemble of n x n unitary matrices -- specifically the characteristic function of the random variable tr(U) -- and combinatorics -- specifically Ulam's problem concerning the…

In a recent study of large non-null sample covariance matrices, a new sequence of functions generalizing the GUE Tracy-Widom distribution of random matrix theory was obtained. This paper derives Painlev\'e formulas of these functions and…

The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlev\'e V system, and the solution of its associated linear isomonodromic system. In…

The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios…

According to Dyson's three fold way, from the viewpoint of global time reversal symmetry there are three circular ensembles of unitary random matrices relevant to the study of chaotic spectra in quantum mechanics. These are the circular…

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…

Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary,…

We consider unitary invariant random matrix ensembles which obey spectral statistics different from the Wigner-Dyson, including unitary ensembles with slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas model. If the…