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Costa, M. and Jordan, J. orcid.org/0000-0003-4686-5440 (Submitted: 2020) Phase transitions in non-linear urns with interacting types. [Preprint - arXiv] (Submitted)
Abstract
We investigate reinforced non-linear urns with interacting types, and show that where there are three interacting types there are phenomena which do not occur with two types. In a model with three types where the interactions between the types are symmetric, we show the existence of a double phase transition with three phases: as well as a phase with an almost sure limit where each of the three colours is equally represented and a phase with almost sure convergence to an asymmetric limit, which both occur with two types, there is also an intermediate phase where both symmetric and asymmetric limits are possible. In a model with anti-symmetric interactions between the types, we show the existence of a phase where the proportions of the three colours cycle and do not converge to a limit, alongside a phase where the proportions of the three colours can converge to a limit where each of the three is equally represented.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Author(s). For reuse permissions, please contact the Author(s). |
Keywords: | math.PR; math.PR |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 25 Jun 2020 07:12 |
Last Modified: | 30 Nov 2022 16:13 |
Status: | Submitted |
Refereed: | Yes |
Identification Number: | 10.48550/arXiv.2006.02685 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162394 |
Available Versions of this Item
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