Convergence of Coalescing Nonsimple Random Walks to The Brownian Web
Dublin Core | PKP Metadata Items | Metadata for this Document | |
1. | Title | Title of document | Convergence of Coalescing Nonsimple Random Walks to The Brownian Web |
2. | Creator | Author's name, affiliation, country | Charles M Newman; Courant Institute of Mathematical Sciences, New York University, New York, NY 10 |
2. | Creator | Author's name, affiliation, country | Krishnamurthi Ravishankar; SUNY-New Paltz, New Paltz, NY 12561, USA |
2. | Creator | Author's name, affiliation, country | Rongfeng Sun; EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlanda |
3. | Subject | Discipline(s) | |
3. | Subject | Keyword(s) | Brownian Web, InvariancePrinciple, Coalescing Random Walks, Brownian Networks, ContinuumLimit. |
3. | Subject | Subject classification | 60K35, 60J65, 60F17,82B41, 60D05 |
4. | Description | Abstract | The Brownian Web (BW) is a family of coalescing Brownian motions starting from every point in space and time $R\times R$. It was first introduced by Arratia, and later analyzed in detail by Toth and Werner. More recently, Fontes, Isopi, Newman and Ravishankar (FINR) gave a characterization of the BW, and general convergence criteria allowing in principle either crossing or noncrossing paths, which they verified for coalescing simple random walks. Later Ferrari, Fontes, and Wu verified these criteria for a two dimensional Poisson Tree. In both cases, the paths are noncrossing. To date, the general convergence criteria of FINR have not been verified for any case with crossing paths, which appears to be significantly more difficult than the noncrossing paths case. Accordingly, in this paper, we formulate new convergence criteria for the crossing paths case, and verify them for non-simple coalescing random walks satisfying a finite fifth moment condition. This is the first time that convergence to the BW has been proved for models with crossing paths. Several corollaries are presented, including an analysis of the scaling limit of voter model interfaces that extends a result of Cox and Durrett. |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | NSF grant DMS-0104278, NSF grant DMS-9803267, NSF grant DMS-0102587 |
7. | Date | (YYYY-MM-DD) | 2005-02-11 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
10. | Identifier | Uniform Resource Identifier | http://ejp.ejpecp.org/article/view/235 |
10. | Identifier | Digital Object Identifier | 10.1214/EJP.v10-235 |
11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 10 |
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
|