Related papers: Gaussian and non-Gaussian fluctuations for mesosco…
In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation and the solution of these equations. We begin by examining…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve…
The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point…
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…
We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
Using numerical diagonalization we study the crossover among different random matrix ensembles [Poissonian, Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE)] realized in two…
We derive exact analytical expressions for correlation functions of singular values of the product of $M$ Ginibre matrices of size $N$ in the double scaling limit $M,N\rightarrow \infty$. The singular value statistics is described by a…
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
In this paper, we study the physics of mesoscopic systems with noninteracting, but fixed number of electrons. From a technical point of view, this means a discussion of the differences between the canonical and the grand canonical ensemble…
We study the Gaussian Unitary Ensemble (GUE) using noncommutative geometry and the homological framework of the Batalin-Vilkovisky (BV) formalism. Coefficients of the correlation functions in the GUE with respect to the rank $N$ are…
In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such…
In this paper, we investigate the crossing statistics of speckle patterns formed in Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend $zero-crossing$ statistics to assess dynamical properties of nanofluid.…
Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows…
We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…
We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals…
We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the thermal equilibrium along the transformation. We derive a general analytic expression for the…