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General Limit Distributions for Sums of Random Variables with a Matrix Product Representation |
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| Authors: | Florian Angeletti Eric Bertin Patrice Abry |
| Institution: | 1. National Institute for Theoretical Physics (NITheP), Stellenbosch, 7600, South Africa 2. Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch, 7600, South Africa 3. Laboratoire Interdisciplinaire de Physique, CNRS UMR 5588, BP 87, Université Joseph Fourier Grenoble, 38402, Saint-Martin d’Hères, France 4. Laboratoire de Physique, ENS Lyon, CNRS, Université de Lyon, 46 Allée d’Italie, 69007, Lyon, France |
| Abstract: | The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions. |
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