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Continuum random cluster and Potts models with Delaunay interactions
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Horrigan, Shannon (2021) Continuum random cluster and Potts models with Delaunay interactions. PhD thesis, University of Warwick.
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WRAP_Theses_Horrigan_2021.pdf - Submitted Version - Requires a PDF viewer. Download (3713Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3728777
Abstract
In this thesis we study a class of marked Gibbsian point processes with geometry dependent interactions known as Delaunay Potts models. We use a random cluster representation to show that a phase transition occurs in one such model for which the interactions depend on the geometry of the triangles which make up the Delaunay triangulation. The random cluster representation relates the finite volume Gibbs distribution to a hyperedge percolation model called the Delaunay random cluster model. We subsequently show that an infinite volume Delaunay random cluster model, as defined by the standard DLR formalism, exists when the potential satisfies two hard-core conditions and the edge weights are uniformly bounded away from 0 and 1.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Gibbs' equation, Cluster analysis, Phase transformations (Statistical physics), Triangle (Geometry) | ||||
Official Date: | 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics and Statistics Doctoral Training Centre | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Adams, Stefan | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | v, 111 leaves : illustrations | ||||
Language: | eng |
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