Related papers: Central and non-central limit theorems in a free p…
We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic…
We describe a family of conservative statistical tests for independence of two autocorrelated time series. The series may take values in any sets, and one of them must be stationary. A user-specified function quantifying the association of…
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered eigenvalues of $M_n$. Under the…
We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…
We proof a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen (Stoch. Dyn. 11, 2011, no. 1),…
In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
Let $G$ be a non--linear function of a Gaussian process $\{X_t\}_{t\in\mathbb{Z}}$ with long--range dependence. The resulting process $\{G(X_t)\}_{t\in\mathbb{Z}}$ is not Gaussian when $G$ is not linear. We consider random wavelet…
We prove that, for general test functions, the limiting behavior of the linear statistic of an independent entry random matrix is determined only by the first four moments of the entry distributions. This immediately generalizes the known…
We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and…
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…
The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to \alpha$, $\alpha>0$, a scaling…
We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to the study of dependent random variables sampled by a $\bbZ$-valued transient random walk. This extends the results…
Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…
We consider a stationary sequence $(X_n)$ constructed by a multiple stochastic integral and an infinite-measure conservative dynamical system. The random measure defining the multiple integral is non-Gaussian, infinitely divisible and has a…
We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…
In this paper we study asymptotic properties of symmetric and non-degenerate random walks on transient hyperbolic groups. We prove a central limit theorem and a law of iterated logarithm for the drift of a random walk, extending previous…
We revisit the central limit theorem for integrated periodograms, equivalently for Toeplitz quadratic forms of stationary Gaussian sequences. Under a regular-variation assumption allowing long-memory singularities and slowly varying…
We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…