Related papers: Spectral Properties of Elementwise-Transformed Spi…
Let $Z_1, \cdots, Z_n$ denote the eigenvalues of the product $\prod_{j=1}^{k_n} \boldsymbol{A}_j$, where $\{\boldsymbol{A}_j\}_{1 \le j \le k_n}$ are independent $n\times n$ complex Ginibre matrices. Define $\alpha = \lim\limits_{n \to…
We study the problem of estimating functions of a large symmetric matrix $A_n$ when we only have access to a noisy estimate $\hat{A}_n=A_n+\sigma Z_n/\sqrt{n}.$ We are interested in the case that $Z_n$ is a Wigner ensemble and suggest an…
The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then…
A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as…
We propose the first fractal frequency mapping, which in a simple form enables to replicate complex neuronal effects. Unlike the conventional filters, which suppress or amplify the input spectral components according to the filter weights,…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
In coherent optical communication systems the laser phase noise is commonly modeled as a Wiener process. We propose a sliding-window based linearization of the phase noise, enabling a novel description. We show that, by stochastically…
We have performed a structural analysis of the Ni K-edge XANES spectrum of a square planar coordination complex, Ni-tetramesitylporphyrin, Ni(II)TMP, in dilute toluene solution. The fit of the spectrum was carried out in the frame of the…
Spectral behaviors of photonic resonators have been the basis for a range of fundamental studies, with applications in classical and quantum technologies. Driven nonlinear resonators provide a fertile ground for phenomena related to phase…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
Some binding-energy-related quantities serving as effective order parameters have been used to analyze the shape phase transition in the odd Sm nuclei. It is found that the signals of phase transition in the odd Sm nuclei are greatly…
Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As…
We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks…
Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schr\"odinger operator is interlaced with that…
This paper considers the recovery of continuous time signals from the magnitude of its samples. It uses a combination of structured modulation and oversampling and provides sufficient conditions on the signal and the sampling system such…
Phase-change materials (PCMs) can switch between different crystalline states as a function of an external bias, offering a pronounced change of their dielectric function. In order to take full advantage of these features for active…
It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to…
Motivated by our previous study of the Twisted Eguchi-Kawai model for non minimal twists, we re-examined the behaviour of the reduced version of the two dimensional principal chiral model. We show that this single matrix model reproduces…
In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…