Related papers: Gaussian and non-Gaussian fluctuations for mesosco…
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…
We report the first observation of the impact of mesoscopic fluctuations on the photocount statistics of coherent light scattered in a random medium. Poisson photocount distribution of the incident light widens and gains additional…
We prove that the fluctuations of mesocopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under…
We are interested in two random matrix ensembles related to permutations: the ensemble of permutation matrices following Ewens' distribution of a given parameter $\theta >0$, and its modification where entries equal to $1$ in the matrices…
We consider global fluctuations of the spectrum of the GUE. Using results on the linear statistics of such matrices as well as variance bounds on the eigenvalues, we show that under a suitable scaling, global fluctuations of the spectrum…
We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the…
We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W\_N$ deformed by a deterministic diagonal perturbation $D\_N$, around a deterministic equivalent which can be expressed in terms of the free convolution…
We establish a central limit theorem for the unnormalized linear statistic of the Gaussian Unitary Ensemble under optimal conditions: the linear statistics converges if and only if the expression for the limiting variance is finite.
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
The unitary group with the Haar probability measure is called Circular Unitary Ensemble. All the eigenvalues lie on the unit circle in the complex plane and they can be regarded as a determinantal point process on $\mathbb{S}^1$. It is also…
We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a…
The currently existing theory of fluorescence correlation spectroscopy(FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in…
Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus…
We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly as $\text{polylog}(m)$) to the extended…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
We consider certain noncolliding interacting particle systems driven by Brownian noise. A key example is drifted Brownian motions conditioned not to intersect and related models of eigenvalues of Hermitian random matrices. We establish…
Carrying out explicitly the computation in a paradigmatic model of non-interacting systems, the Gaussian Model, we show the existence of a singular point in the probability distribution $P(M)$ of an extensive variable $M$. Interpreting…
Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…