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Rigorous computation of diffusion coefficients for expanding maps
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Pollicott, Mark, Jenkinson, Oliver and Vytnova, Polina (2018) Rigorous computation of diffusion coefficients for expanding maps. Journal of Statistical Physics, 170 (2). pp. 221-253. doi:10.1007/s10955-017-1930-8 ISSN 0022-4715.
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Official URL: https://doi.org/10.1007/s10955-017-1930-8
Abstract
For real analytic expanding interval maps, a novel method is given for rigorously approximating the diffusion coefficient of real analytic observables. As a theoretical algorithm, our approximation scheme is shown to give quadratic exponential convergence to the diffusion coefficient. The method for converting this rapid convergence into explicit high precision rigorous bounds is illustrated in the setting of Lanford’s map x↦2x+12x(1−x)(mod1) .
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Number theory, Mappings (Mathematics) | ||||||||
Journal or Publication Title: | Journal of Statistical Physics | ||||||||
Publisher: | Springer New York LLC | ||||||||
ISSN: | 0022-4715 | ||||||||
Official Date: | January 2018 | ||||||||
Dates: |
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Volume: | 170 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 221-253 | ||||||||
DOI: | 10.1007/s10955-017-1930-8 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 5 December 2017 | ||||||||
Date of first compliant Open Access: | 6 March 2018 |
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