Journal article
On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions
- Abstract:
- The objective of this article is to analyse the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We focus our attention on the combined mean field and diffusive (homogenisation) limits. In particular, we show that these two limits do not commute if the mean field system constrained to the torus undergoes a phase transition, that is to say, if it admits more than one steady state. A typical example of such a system on the torus is given by the noisy Kuramoto model of mean field plane rotators. As a by-product of our main results, we also analyse the energetic consequences of the central limit theorem for fluctuations around the mean field limit and derive optimal rates of convergence in relative entropy of the Gibbs measure to the (unique) limit of the mean field energy below the critical temperature.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 893.6KB, Terms of use)
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- Publisher copy:
- 10.1007/s00205-021-01648-1
Authors
- Publisher:
- Springer
- Journal:
- Archive for Rational Mechanics and Analysis More from this journal
- Volume:
- 24
- Pages:
- 91-148
- Publication date:
- 2021-04-25
- Acceptance date:
- 2021-03-12
- DOI:
- EISSN:
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1432-0673
- ISSN:
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0003-9527
- Language:
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English
- Keywords:
- Pubs id:
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1167106
- Local pid:
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pubs:1167106
- Deposit date:
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2021-03-12
- ARK identifier:
Terms of use
- Copyright holder:
- Delgadino et al.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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