Norris, J., Silvestri, V. and Turner, A. orcid.org/0000-0002-6015-5392 (2024) Stability of regularized Hastings-Levitov aggregation in the subcritical regime. Communications in Mathematical Physics, 405. 74. ISSN 0010-3616
Abstract
We prove bulk scaling limits and fluctuation scaling limits for a two-parameter class ALE(α, η) of continuum planar aggregation models. The class includes regularized versions of the Hastings–Levitov family HL(α) and continuum versions of the family of dielectric-breakdown models, where the local attachment intensity for new particles is specified as a negative power −η of the density of arc length with respect to harmonic measure. The limit dynamics follow solutions of a certain Loewner–Kufarev equation, where the driving measure is made to depend on the solution and on the parameter ζ = α + η. Our results are subject to a subcriticality condition ζ ≤ 1: this includes HL(α) for α ≤ 1 and also the case α = 2, η = −1 corresponding to a continuum Eden model. Hastings and Levitov predicted a change in behaviour for HL(α) at α = 1, consistent with our results. In the regularized regime considered, the fluctuations around the scaling limit are shown to be Gaussian, with independent Ornstein–Uhlenbeck processes driving each Fourier mode, which are seen to be stable if and only if ζ ≤ 1.
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Copyright, Publisher and Additional Information: | © The Author(s) 2024. 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. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Feb 2024 11:58 |
Last Modified: | 18 Mar 2024 10:12 |
Published Version: | https://link.springer.com/article/10.1007/s00220-0... |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s00220-024-04960-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208971 |
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