Related papers: Spectral statistics for quantized skew translation…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to…
We consider a simple model of partially expanding map on the torus. We study the spectrum of the Ruelle transfer operator and show that in the limit of high frequencies in the neutral direction (this is a semiclassical limit), the spectrum…
In this paper, we investigate the Moore-Penrose inversion of a simple connected graph. We analyze qualitative, statistical, and extreme properties of spectral indices of signable pseudo-invertible graphs. We introduce and analyze a wide…
In this paper we study the multiple ergodic averages $$ \frac{1}{n}\sum_{k=1}^n \varphi(x_k, x_{kq}, ..., x_{k q^{\ell-1}}), \qquad (x_n) \in \Sigma_m $$ on the symbolic space $\Sigma_m ={0, 1, ..., m-1}^{\mathbb{N}^*}$ where $m\ge 2,…
The spectral fluctuation properties of spherical nuclei are considered by use of NNSD statistic. With employing a generalized Brody distribution included Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters are…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
We study linear random walks on the torus and show a quantitative equidistribution statement, under the assumption that the Zariski closure of the acting group is semisimple.
The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the…
We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that…
The Szekeres metric is an inhomogeneous cosmological model without any symmetries. The standard Riemann-type coordinates can be transformed into spherical-type coordinates, but the metric is no longer diagonal, and the constant "radius"…
This paper discusses a general method for spectral type theorems using metric spaces instead of vector spaces. Advantages of this approach are that it applies to genuinely non-linear situations and also to random versions. Metric analogs of…
This paper investigates the distribution of marks obtained by students across multiple courses to explore whether the data conforms to a skew-normal distribution. Traditional methods for assessing normality, such as the Shapiro Wilk test,…
This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from $\alpha$-regularly varying populations with general covariance structures. By…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
The logarithmic Chow semistability is a notion of Geometric Invariant Theory for the pair consists of varieties and its divisors. In this paper we introduce a obstruction of semistability for polarized toric manifolds and its toric…
For smooth random dynamical systems we consider the quenched linear and higher-order response of equivariant physical measures to perturbations of the random dynamics. We show that the spectral perturbation theory of Gou\"ezel, Keller, and…
We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global $U(1)$ cosmic strings, or equivalently vortices in superfluid $^4$He. We use a new method which avoids the specification of…
We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…