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Central limit theorems and suppression of anomalous diffusion for systems with symmetry
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Gottwald, Georg A. and Melbourne, Ian (2016) Central limit theorems and suppression of anomalous diffusion for systems with symmetry. Nonlinearity, 29 (10). 2941. doi:10.1088/0951-7715/29/10/2941 ISSN 0951-7715.
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Official URL: http://dx.doi.org/10.1088/0951-7715/29/10/2941
Abstract
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle/functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps. In particular, our results include situations where the central limit theorem would fail, and anomalous behaviour would prevail, if the compact group were not present. This has important consequences for systems with noncompact Euclidean symmetry and provides the rigorous proof for a conjecture made in our paper: a Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Gottwald and Melbourne (2013 Proc. Natl Acad. Sci. USA 110 8411–6).
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Brownian motion processes, Huygens' principle | ||||||||
| Journal or Publication Title: | Nonlinearity | ||||||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||||||
| ISSN: | 0951-7715 | ||||||||
| Official Date: | 17 August 2016 | ||||||||
| Dates: |
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| Volume: | 29 | ||||||||
| Number: | 10 | ||||||||
| Article Number: | 2941 | ||||||||
| DOI: | 10.1088/0951-7715/29/10/2941 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 25 August 2016 | ||||||||
| Date of first compliant Open Access: | 12 August 2017 | ||||||||
| Funder: | Australian Research Council (ARC), Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC) | ||||||||
| Grant number: | EP/F031807/1 (EPSRC), AdG 320977 (ERC) |
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