Ergodicity of avalanche transformations |
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| Authors: | Manfred Denker Ana Rodrigues |
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| Affiliation: | 1. Mathematics Department, Pennsylvania State University, State College, PA 16802, USA;2. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, Streatham Campus, North Park Road, Exeter EX4 4QF, UK |
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| Abstract: | In this paper, we study dynamical systems of product type and some particular inducing scheme motivated by neural dynamics (called avalanche transformation). We derive the distribution of avalanche sizes and give sufficient conditions such that the avalanche transformation is ergodic. Moreover, we deduce a multivariate central limit theorem as a corollary. In memoriam: Wenbo V. Li (1963–2013) |
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| Keywords: | avalanche transformation ergodicity induced transformation Cayley's theorem central limit theorem |
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