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arXiv · 1712.03619

Central Limit Theorems for a Stationary Semicircular Sequence in Free Probability

Zhichao Wang
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Abstract

In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we can get a central-limit result via Hermite polynomials and the diagram formula for cumulants. In this paper, the main result is an analogous central limit theorem, in a free probability setting, for real-valued functionals of a stationary semicircular sequence with long-range dependence, namely the correlation function of the underlying time series tends to zero as the lag goes to infinity.

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Zhichao Wang. 2017-12-11. Central Limit Theorems for a Stationary Semicircular Sequence in Free Probability. https://arxiv.org/abs/1712.03619

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