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One-dimensional Voter Model Interface Revisited

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	One-dimensional Voter Model Interface Revisited
2.	Creator	Author's name, affiliation, country	Siva R Athreya; Indian Statistical Institute; India
2.	Creator	Author's name, affiliation, country	Rongfeng Sun; National University of Singapore; Singapore
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	voter model interface, measure-valued process, tightness
3.	Subject	Subject classification	60K35, 82C22, 82C24, 60F17
4.	Description	Abstract	We consider the voter model on $\mathbb{Z}$, starting with all 1's to the left of the origin and all $0$'s to the right of the origin. It is known that if the associated random walk kernel $p$ has zero mean and a finite r-th moment for any $r>3$, then the evolution of the boundaries of the interface region between 1's and 0's converge in distribution to a standard Brownian motion $(B_t)_{t>0}$ under diffusive scaling of space and time. This convergence fails when $p$ has an infinite $r$-th moment for any $r<3$, due to the loss of tightness caused by a few isolated $1$'s appearing deep within the regions of all $0$'s (and vice versa) at exceptional times. In this note, we show that as long as $p$ has a finite second moment, the measure-valued process induced by the rescaled voter model configuration is tight, and converges weakly to the measure-valued process $1_{x< B_t} dx$, $t>0$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	National University of Singapore
7.	Date	(YYYY-MM-DD)	2011-12-07
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1688
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1688
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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