Related papers: The strong mixing and the operator-selfdecomposabi…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space $\mR^{m+1}$ was recently constructed, including a higher dimensional analogue of the logarithmic function in the…
We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the…
It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility…
We study topologizability and power boundedness of weigh\-ted composition operators on (certain subspaces of) $\mathscr{D}'(X)$ for an open subset $X$ of $\mathbb{R}^d$. For the former property we derive a characterization in terms of the…
We consider a Schroedinger operator with random potential distributed according to a Poisson process. We show that expectations of matrix elements of the resolvent as well as the density of states can be approximated to arbitrary precision…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…
We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $E\subset\Bbb N\cup\{\infty\}$ as the set of essential…
Let $A$ be a self-adjoint operator acting over a space $X$ endowed with a partition. We give lower bounds on the energy of a mixed state $\rho$ from its distribution in the partition and the spectral density of $A$. These bounds improve…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group ${T_t}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
We construct universal mixers, incompressible flows that mix arbitrarily well general solutions to the corresponding transport equation, in all dimensions. This mixing is exponential in time (i.e., essentially optimal) for any initial…
While on the one hand, chaotic dynamical systems can be predicted for all time given exact knowledge of an initial state, they are also in many cases rapidly mixing, meaning that smooth probabilistic information (quantified by measures) on…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…