Ergodicity of avalanche transformations

Manfred Denker; Ana Rodrigues

doi:10.1080/14689367.2014.947244

Ergodicity of avalanche transformations

Manfred Denker, Ana Rodrigues

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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)1 A few weeks before his sudden death on 26 January 2013 we received a comment on this paper which is reproduced at the end of this paper.

Original language	English (US)
Pages (from-to)	517-536
Number of pages	20
Journal	Dynamical Systems
Volume	29
Issue number	4
DOIs	https://doi.org/10.1080/14689367.2014.947244
State	Published - Oct 2 2014

All Science Journal Classification (ASJC) codes

Mathematics(all)
Computer Science Applications

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10.1080/14689367.2014.947244

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AB - 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)1 A few weeks before his sudden death on 26 January 2013 we received a comment on this paper which is reproduced at the end of this paper.

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Ergodicity of avalanche transformations

Abstract

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