One-dimensional interacting particle systems as Pfaffian point processes
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 wa...
Main Author: | |
---|---|
Published: |
University of Warwick
2016
|
Subjects: | |
Online Access: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.693235 |
id |
ndltd-bl.uk-oai-ethos.bl.uk-693235 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-bl.uk-oai-ethos.bl.uk-6932352018-02-05T15:35:51ZOne-dimensional interacting particle systems as Pfaffian point processesGarrod, Barnaby G.2016A 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.516.3QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.693235http://wrap.warwick.ac.uk/81054/Electronic Thesis or Dissertation |
collection |
NDLTD |
sources |
NDLTD |
topic |
516.3 QA Mathematics |
spellingShingle |
516.3 QA Mathematics Garrod, Barnaby G. One-dimensional interacting particle systems as Pfaffian point processes |
description |
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. |
author |
Garrod, Barnaby G. |
author_facet |
Garrod, Barnaby G. |
author_sort |
Garrod, Barnaby G. |
title |
One-dimensional interacting particle systems as Pfaffian point processes |
title_short |
One-dimensional interacting particle systems as Pfaffian point processes |
title_full |
One-dimensional interacting particle systems as Pfaffian point processes |
title_fullStr |
One-dimensional interacting particle systems as Pfaffian point processes |
title_full_unstemmed |
One-dimensional interacting particle systems as Pfaffian point processes |
title_sort |
one-dimensional interacting particle systems as pfaffian point processes |
publisher |
University of Warwick |
publishDate |
2016 |
url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.693235 |
work_keys_str_mv |
AT garrodbarnabyg onedimensionalinteractingparticlesystemsaspfaffianpointprocesses |
_version_ |
1718613170099060736 |