Related papers: On the Spectral Form Factor for Random Matrices
Using his formulation of the potential theoretic notion of balayage and his deep results about this idea, Beurling gave sufficient conditions for Fourier frames in terms of balayage. The analysis makes use of spectral synthesis, due to…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Recently we have developed a method called ``Symmetry Finder'' (SF) for hunting the reparametrization symmetry in the three-neutrino system in matter. Here, we apply SF to the Denton {\it et al.} (DMP) perturbation theory extended by…
Consider $N\times N$ Hermitian or symmetric random matrices $H$ where the distribution of the $(i,j)$ matrix element is given by a probability measure $\nu_{ij}$ with a subexponential decay. Let $\sigma_{ij}^2$ be the variance for the…
We prove that the distribution of eigenvectors of generalized Wigner matrices is universal both in the bulk and at the edge. This includes a probabilistic version of local quantum unique ergodicity and asymptotic normality of the…
We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from…
We consider a multichannel wire with a disordered region of length $L$ and a reflecting boundary. The reflection of a wave of frequency $\omega$ is described by the scattering matrix $\mathcal{S}(\omega)$, encoding the probability…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel dimensionality reduction methodology for $n$-dimensional random fields observed across a number $S$ spatial locations and $T$ time periods. We call…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral…
Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify ``ergodicity'', including the presence of underlying macroscopic symmetries, in generic quantum systems…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
We study the spectral properties of a multiparametric system having particle-hole symmetry in random matrix setting. We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
The deformed Fourier matrices $H=F_M\otimes_QF_N$, with $Q\in\mathbb T^{MN}$, produce a matrix model $C(S_{MN}^+)\to M_{MN}(C(\mathbb T^{MN}))$. When $Q\in\mathbb T^{MN}$ is generic, the corresponding fiber can be investigated via algebraic…
Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution for machine learning applications. This famous technique, known as Random Fourier…
Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by…