Quantum central limit theorems for weakly dependent maps I

Central Limit Theorems for Dependent Random Variables

1. Limiting distributions of sums of 'small' independent random variables have been extensively studied and there is a satisfactory general theory of the subject (see e.g. the monograph of B.V. Gnedenko and A.N. Kolmogorov [2]). These results are conveniently formulated for double arrays Xn k (k = 1, . . . , kn ; n = 1, 2, . . . ) of random variables where the Xn k (k = 1, . . . , kn), the rand...

Central limit theorems for the excursion sets volumes of weakly dependent random fields

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi–associated random fields on R are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed. AMS 2000 subject ...

Central Limit Theorems for Non-invertible Measure Preserving Maps

This paper is motivated by the question “How can we produce the characteristics of a Wiener process (Brownian motion) from a semi-dynamical system?”. This question is intimately connected with Central Limit Theorems for non-invertible maps and various invariance principles. Many results on CLT and invariance principles for maps have been proved, see e.g. the surveys Denker [4] and Mackey and Ty...

Central Limit Theorems for Open Quantum Random Walks∗

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in Quantum Information Theory (such as the well-known Hadamard random...

Central Limit Theorems For Dependent, Heterogeneous Processes With Trending Moments