Indexing metadata

Convergence Results and Sharp Estimates for the Voter Model Interfaces


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Convergence Results and Sharp Estimates for the Voter Model Interfaces
 
2. Creator Author's name, affiliation, country Samir Belhaouari; EPFL
 
2. Creator Author's name, affiliation, country Thomas Mountford; EPFL
 
2. Creator Author's name, affiliation, country Rongfeng Sun; EURANDOM
 
2. Creator Author's name, affiliation, country Glauco Valle; EPFL / DME-IM-UFRJ
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) voter model interface, coalescing random walks, Brownian web, invariance principle
 
3. Subject Subject classification 60K35, 82B24, 82B41, 60F17
 
4. Description Abstract 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 $\gamma$-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 $\gamma$-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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) R. Sun was supported by a RDSES short visit grant from European Science Foundation
 
7. Date (YYYY-MM-DD) 2006-08-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/349
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-349
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.