Local limit theorem for large deviations and statistical box-tests

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Central and Local Limit Theories in Markov Dependent Random Variables

Dynamic Quantum Bernoulli Random Walks

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviations principl...

Large deviations of combinatorial distributions II: Local limit theorems

This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we a...

Se p 20 06 LIMIT THEOREMS FOR COUPLED INTERVAL MAPS

We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding interval maps. The core of the paper is a proof that the spectral radii of the Fourier-transfer operators for such a system are strictly less than 1. This extends the approach of [KL06] where the ordinary transfer operator was studied. 1. Results This paper deals with the issue...