Related papers: Eigenvalue processes of Elliptic Ginibre Ensemble …
This is part II of a review relating to the three classes of random non-Hermitian Gaussian matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre unitary ensemble) case of complex elements, in this…
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
For a given normalized Gaussian symmetric matrix-valued process $Y^{(n)}$, we consider the process of its eigenvalues $\{(\lambda_{1}^{(n)}(t),\dots, \lambda_{n}^{(n)}(t)); t\ge 0\}$ as well as its corresponding process of empirical…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
By studying the two-time overlap correlation function, we give a comprehensive analysis of the phase diagram of the Random Hopping Dynamics of the Random Energy Model (REM) on time-scales that are exponential in the volume. These results…
We consider an ensemble of self-dual matrices with arbitrary complex entries. This ensemble is closely related to a previously defined ensemble of anti-symmetric matrices with arbitrary complex entries. We study the two-level correlation…
We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is the complex matrix with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix (it can be random and in this case it is independent of $H_0$). Assuming…
We study inter-chain pair tunnelling dynamics based on an exact two-particle solution for a two-leg ladder. We show that the Hermitian Hamiltonian shares a common two-particle eigenstate with a corresponding non-Hermitian Hubbard…
The numerical range of a non-normal matrix plays a central role as a descriptor of non-normal effects beyond spectral information. We study a class of fundamental non-Hermitian random matrix ensembles that interpolate between the Hermitian…
We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of…
We consider a system of noncolliding Brownian motions introduced in our previous paper, in which the noncolliding condition is imposed in a finite time interval $(0,T]$. This is a temporally inhomogeneous diffusion process whose transition…
In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
For the class of Gauss-Markov processes we study the problem of asymptotic equivalence of the nonparametric regression model with errors given by the increments of the process and the continuous time model, where a whole path of a sum of a…
The Ginibre point process is given by the eigenvalue distribution of a non-hermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the complex plane ${\mathbb{C}}$ in the sense…
Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…
We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space…
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show…