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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2006
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| Subjects: | |
| Online Access: | http://scholars.utp.edu.my/id/eprint/2714/ http://scholars.utp.edu.my/id/eprint/2714/1/Samir_brahim_paper_2.pdf |
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| author | Brahim Belhaouari, samir Mountford, Thomas |
| author_facet | Brahim Belhaouari, samir Mountford, Thomas |
| author_sort | Brahim Belhaouari, samir |
| building | UTP Institutional Repository |
| collection | Online Access |
| 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 |
| first_indexed | 2025-11-13T07:28:05Z |
| format | Article |
| id | oai:scholars.utp.edu.my:2714 |
| institution | Universiti Teknologi Petronas |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-13T07:28:05Z |
| publishDate | 2006 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:scholars.utp.edu.my:27142017-01-19T08:27:22Z http://scholars.utp.edu.my/id/eprint/2714/ 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 en http://scholars.utp.edu.my/id/eprint/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 |
| 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 |
| title | 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_short | Convergence results and sharp estimates for the
voter model interfaces |
| title_sort | convergence results and sharp estimates for the
voter model interfaces |
| topic | RZ Other systems of medicine QA75 Electronic computers. Computer science |
| url | http://scholars.utp.edu.my/id/eprint/2714/ http://scholars.utp.edu.my/id/eprint/2714/1/Samir_brahim_paper_2.pdf |