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Horizontal curves of hyperbolic metrics
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Rupflin, Melanie and Topping, Peter (2018) Horizontal curves of hyperbolic metrics. Calculus of Variations and Partial Differential Equations, 57 . 106. doi:10.1007/s00526-018-1386-y ISSN 0944-2669.
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Official URL: https://doi.org/10.1007/s00526-018-1386-y
Abstract
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under generic growth conditions on particle jump rates, and the limit provides a master equation for the single site dynamics of the particle system, which is a non-linear birth death chain. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary distributions. Our findings are consistent with recent results on exchange driven growth, and provide a connection between the well studied phenomena of gelation and condensation.We analyse the fine convergence properties of one parameter families of hyperbolic metrics that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms. Such families arise naturally in the study of general curves of metrics on surfaces, and in one of the gradients flows for the harmonic map energy.
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): | Geometry, Curves, Algebraic | ||||||||
Journal or Publication Title: | Calculus of Variations and Partial Differential Equations | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0944-2669 | ||||||||
Official Date: | August 2018 | ||||||||
Dates: |
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Volume: | 57 | ||||||||
Article Number: | 106 | ||||||||
DOI: | 10.1007/s00526-018-1386-y | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 14 May 2018 | ||||||||
Date of first compliant Open Access: | 14 September 2018 | ||||||||
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