Related papers: The linearization of the central limit operator in…
We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
In this paper free harmonic analysis tools are used to study parabolic iteration in the complex upper half-plane. The main result here is a complete characterization for the norming constants in the monotonic central limit theorem. This…
The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
Data processing lower bounds on the expected distortion are derived in the finite-alphabet semi-deterministic setting, where the source produces a deterministic, individual sequence, but the channel model is probabilistic, and the decoder…
We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.
In this paper, we obtain the central limit theorems for LS estimator in simple linear errors-in-variables (EV) regression models under some mild conditions. And we also show that those conditions are necessary in some sense.
Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators…
We give error estimates in Peng's central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only…
We apply methods of the fixed point theory to a Lambda policy iteration with a randomization algorithm for weak contractions mappings. This type of mappings covers a broader range than the strong contractions typically considered in the…
We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…
A conjugation $C$ is an anti-linear isometric involution on a complex Hilbert space $\clh$, and $T\in \clb(\clh)$ is conjugate normal if $T^*T = CTT^*C$ holds for some conjugation (C). In this paper, we provide a factorization and range…
We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal…
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…
By means of a fixed point method we discuss the deformation of operator means and multivariate means of positive definite matrices/operators. It is shown that the deformation of an operator mean becomes again an operator mean. The means…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
We deduce sufficient conditions for the Central Limit Theorem (CLT) in the Lebesgue-Riesz space L(p) defined on some measure space for the sequence of centered random variables satisfying the strong mixing (Rosenblatt) condition. We…