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Convergence of Coalescing Nonsimple Random Walks to The Brownian Web


 
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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 PDF
 
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
 
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