Related papers: Mock-Gaussian Behaviour for Linear Statistics of C…

We prove Gaussian fluctuation for pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(\theta_i-\theta_j)$ for the Circular Unitary Ensemble (CUE) of random matrices in the case of a slowly growing variance in the limit of…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly.…

For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.

We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…

In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions…

We calculate the higher order moments in a sequence of models where the initial density fluctuations are drawn from a chi^2_nu distribution with a power-law power spectrum. For large values of nu the distribution is approximately gaussian,…

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…

We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from Gaussian unitary ensemble and $W$ is a deterministic diagonal matrix with positive entries. Using…

We present here an elementary example, for every fixed positive integer $k,$ of a strictly stationary nongaussian stochastic process in discrete time, all of whose $k$-marginals are gaussian.

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. Using a procedure inspired by the similar, but continuous case of jet fragmentation in QCD, this discretized process may be analyzed…

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here we present a systematic study of such characteristics for the Polish stock market index…

We experiment with some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We look at matrices defined by Gaussian primes and look at the growth of the…

In [earlier work by the author], it was shown that if U is a random n x n unitary matrix, then for any p>=n, the eigenvalues of U^p are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens…

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could…

In Puplinskaite and Surgailis (2014) we introduced the notion of scaling transition for stationary random fields $X$ on $\mathbb{Z}^2$ in terms of partial sums limits, or scaling limits, of $X$ over rectangles whose sides grow at possibly…

Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…

We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are…