相关论文: Saturation of number variance in embedded random m…

Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behaviour of a system as exemplified by the emergence of…

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…

We investigate the random matrix configurations for two or three interacting electrons in one-dimensional disordered systems. In a suitable non-interacting localized electron basis we obtain a sparse random matrix with very long tails which…

Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales.…

We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the…

The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…

We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing…

We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…

We numerically analyse the density field of three-dimensional randomly jammed packings of monodisperse soft frictionles spherical particles, paying special attention to fluctuations occurring at large lengthscales. We study in detail the…

We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…

We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of…

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 study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as…

We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…

We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…

The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…

We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…

We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…

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…

Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…