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Convergence results and sharp estimates for the voter model interfaces

We study the evolution of the interface for the one-dimensional voter model. We show that if the random walk kernel associated with the voter model has finite th moment for some gamma > 3, then the evolution of the interface boundaries converge weakly to a Brownian motion under diffusive scal...

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Main Authors: Brahim Belhaouari, samir, Mountford, Thomas
Format: Article
Published: 2006
Subjects:
RZ Other systems of medicine
QA75 Electronic computers. Computer science
Online Access:http://eprints.utp.edu.my/2714/1/Samir_brahim_paper_2.pdf
http://eprints.utp.edu.my/2714/
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spelling my.utp.eprints.27142017-01-19T08:27:22Z Convergence results and sharp estimates for the voter model interfaces Brahim Belhaouari, samir Mountford, Thomas RZ Other systems of medicine QA75 Electronic computers. Computer science We study the evolution of the interface for the one-dimensional voter model. We show that if the random walk kernel associated with the voter model has finite th moment for some gamma > 3, then the evolution of the interface boundaries converge weakly to a Brownian motion under diffusive scaling. This extends recent work of Newman, Ravishankar and Sun. Our result is optimal in the sense that finite th moment is necessary for this convergence for all gamma in (0, 3). We also obtain relatively sharp estimates for the tail distribution of the size of the equilibrium interface, extending earlier results of Cox and Durrett, and Belhaouari, Mountford and Valle 2006 Article PeerReviewed application/pdf http://eprints.utp.edu.my/2714/1/Samir_brahim_paper_2.pdf Brahim Belhaouari, samir and Mountford, Thomas (2006) Convergence results and sharp estimates for the voter model interfaces. E l e c t r o n i c J o u r n a l o f P r o b a b i l i t y (30). pp. 768-801. ISSN ELECTRONIC JOURNAL OF PROBABILITY http://eprints.utp.edu.my/2714/
institution Universiti Teknologi Petronas
building UTP Resource Centre
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Petronas
content_source UTP Institutional Repository
url_provider http://eprints.utp.edu.my/
topic RZ Other systems of medicine
QA75 Electronic computers. Computer science
spellingShingle RZ Other systems of medicine
QA75 Electronic computers. Computer science
Brahim Belhaouari, samir
Mountford, Thomas
Convergence results and sharp estimates for the voter model interfaces
description We study the evolution of the interface for the one-dimensional voter model. We show that if the random walk kernel associated with the voter model has finite th moment for some gamma > 3, then the evolution of the interface boundaries converge weakly to a Brownian motion under diffusive scaling. This extends recent work of Newman, Ravishankar and Sun. Our result is optimal in the sense that finite th moment is necessary for this convergence for all gamma in (0, 3). We also obtain relatively sharp estimates for the tail distribution of the size of the equilibrium interface, extending earlier results of Cox and Durrett, and Belhaouari, Mountford and Valle
format Article
author Brahim Belhaouari, samir
Mountford, Thomas
author_facet Brahim Belhaouari, samir
Mountford, Thomas
author_sort Brahim Belhaouari, samir
title Convergence results and sharp estimates for the voter model interfaces
title_short Convergence results and sharp estimates for the voter model interfaces
title_full Convergence results and sharp estimates for the voter model interfaces
title_fullStr Convergence results and sharp estimates for the voter model interfaces
title_full_unstemmed Convergence results and sharp estimates for the voter model interfaces
title_sort convergence results and sharp estimates for the voter model interfaces
publishDate 2006
url http://eprints.utp.edu.my/2714/1/Samir_brahim_paper_2.pdf
http://eprints.utp.edu.my/2714/
_version_ 1738655214117847040
score 13.160551

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