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 |
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Department of Mathematics, University of Washington, Seattle, USA
2006
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| Online Access: | http://scholars.utp.edu.my/id/eprint/2718/ http://scholars.utp.edu.my/id/eprint/2718/1/Samir_brahim_paper_2.pdf |
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| author | B. Belhouari, Samir Mountford, Thomas Sun, Rongfeng Valle, G. |
| author_facet | B. Belhouari, Samir Mountford, Thomas Sun, Rongfeng Valle, G. |
| author_sort | B. Belhouari, 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 | 2025-11-13T07:28:06Z |
| format | Article |
| id | oai:scholars.utp.edu.my:2718 |
| institution | Universiti Teknologi Petronas |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-13T07:28:06Z |
| publishDate | 2006 |
| publisher | Department of Mathematics, University of Washington, Seattle, USA |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:scholars.utp.edu.my:27182017-01-19T08:27:22Z http://scholars.utp.edu.my/id/eprint/2718/ Convergence results and sharp estimates for the voter model interfaces B. Belhouari, Samir Mountford, Thomas Sun, Rongfeng Valle, G. 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 Department of Mathematics, University of Washington, Seattle, USA 2006 Article PeerReviewed application/pdf en http://scholars.utp.edu.my/id/eprint/2718/1/Samir_brahim_paper_2.pdf B. Belhouari, Samir and Mountford, Thomas and Sun, Rongfeng and Valle, G. (2006) Convergence results and sharp estimates for the voter model interfaces. ELECTRONIC JOURNAL OF PROBABILITY, 11 (30). pp. 768-801. ISSN 1083-6489 |
| spellingShingle | RZ Other systems of medicine QA75 Electronic computers. Computer science B. Belhouari, Samir Mountford, Thomas Sun, Rongfeng Valle, G. 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/2718/ http://scholars.utp.edu.my/id/eprint/2718/1/Samir_brahim_paper_2.pdf |