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 scali...
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Institute of Mathematical Statistics.
2010
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my.utp.eprints.27212017-01-19T08:25:03Z Convergence results and sharp estimates for the voter model interfaces brahim belhaouari, samir Thomas Mountford, TM G. Valle, GV 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 gamm 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 Institute of Mathematical Statistics. 2010 Citation Index Journal PeerReviewed application/pdf http://eprints.utp.edu.my/2721/1/Samir_brahim_paper_2.pdf brahim belhaouari, samir and Thomas Mountford, TM and G. Valle, GV (2010) Convergence results and sharp estimates for the voter model interfaces. [Citation Index Journal] http://eprints.utp.edu.my/2721/ |
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QA75 Electronic computers. Computer science brahim belhaouari, samir Thomas Mountford, TM G. Valle, GV 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 gamm 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 |
Citation Index Journal |
| author |
brahim belhaouari, samir Thomas Mountford, TM G. Valle, GV |
| author_facet |
brahim belhaouari, samir Thomas Mountford, TM G. Valle, GV |
| 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 |
| publisher |
Institute of Mathematical Statistics. |
| publishDate |
2010 |
| url |
http://eprints.utp.edu.my/2721/1/Samir_brahim_paper_2.pdf http://eprints.utp.edu.my/2721/ |
| _version_ |
1738655215093022720 |
| score |
13.251813 |