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One-dimensional interacting particle systems as Pfaffian point processes
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Garrod, Barnaby G. (2016) One-dimensional interacting particle systems as Pfaffian point processes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2876155~S1
Abstract
A wide class of one-dimensional continuous-time discrete-space interacting particle systems are shown to be Pfaffian point processes at fixed times with kernels characterised by the solutions to associated two-dimensional ODEs. The models comprise instantaneously coalescing or annihilating random walks with fully spatially inhomogeneous jump rates and deterministic initial conditions, including additional pairwise immigration or branching in the pure interaction regimes. We formulate convergence of Pfaffian point processes via their kernels, enabling investigation of diffusive scaling limits, which boils down uniform convergence of lattice approximations to two-dimensional PDEs. Convergence to continuum point processes is developed for a subset of the discrete models. Finally, in the case of annihilating random walks with pairwise immigration we extend the picture to multiple times, establishing the extended Pfaffian property for the temporal process.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Pfaffian systems | ||||
Official Date: | May 2016 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Tribe, Roger ; Zaboronski, Oleg | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Extent: | vi, 153 leaves | ||||
Language: | eng |
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