Related papers: Critical edge statistics for deformed GinUEs
This paper reports on the experimental observation of topologically protected edge state and exceptional point in an open and Non-Hermitian system. While the theoretical underpinning is generic to wave physics, the simulations and…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
Basing on our recent results on the $1/n$-expansion in unitary invariant random matrix ensembles, known as matrix models, we prove that the local eigenvalue statistic, arising in a certain neighborhood of the edges of the support of the…
Generically, spectral statistics of spinless systems with time reversal invariance (TRI) and chaotic dynamics are well described by the Gaussian Orthogonal ensemble (GOE). However, if an additional symmetry is present, the spectrum can be…
We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE universality class from random matrix theory.
Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint…
Girko matrices have independent and identically distributed entries of mean zero and unit variance. In this note, we consider the random matrix model formed by the ratio of two independent Girko matrices, its entries are dependent and…
We illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point…
We investigate the spectral properties of a generalized GOE (Gaussian Orthogonal Ensemble) capable of describing critical statistics. The joint distribution of eigenvalues of this model is expressed as the diagonal element of the density…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
We compare the Ornstein-Uhlenbeck process for the Gaussian Unitary Ensemble to its non-hermitian counterpart - for the complex Ginibre ensemble. We exploit the mathematical framework based on the generalized Green's functions, which…
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…
A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace…
Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of…
The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecutive eigenvalues at the spectral edges has received little…
The real Ginibre ensemble refers to the family of $n\times n$ matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges…
The critical exponents of continuous phase transitions of a Hermitian system depend on and only on its dimensionality and symmetries. This is the celebrated notion of the universality of continuous phase transitions. Here we report the…
Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime…
In this paper, we survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner Hermitian random matrix ensembles, focusing on the Four Moment Theorem and its refinements and applications,…