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The Center of Mass for Spatial Branching Processes and an Application for Self-Interaction

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The Center of Mass for Spatial Branching Processes and an Application for Self-Interaction
2.	Creator	Author's name, affiliation, country	Janos Englander; University of Colorado at Boulder; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Branching Brownian motion; super-Brownian motion; center of mass; self-interaction; Curie-Weiss model; McKean-Vlasov limit; branching Ornstein-Uhlenbeck process; spatial branching processes; H-transform
3.	Subject	Subject classification	Primary: 60J60; Secondary: 60J80
4.	Description	Abstract	Consider the center of mass of a supercritical branching-Brownian motion. In this article we first show that it is a Brownian motion being slowed down such that it tends to a limiting position almost surely, and that this is also true for a model where the branching-Brownian motion is modified by attraction/repulsion between particles.  We then put this observation together with the description of the interacting system as viewed from its center of mass, and get the following asymptotic behavior: the system asymptotically becomes a branching Ornstein-Uhlenbeck process (inward for attraction and outward for repulsion), but (i) the origin is shifted to a random point which has normal distribution, and (ii) the Ornstein-Uhlenbeck particles are not independent but constitute a system with a degree of freedom which is less than their number by precisely one.  The main result of the article then is a scaling limit theorem for the local mass, in the attractive case. A conjecture is stated for the behavior of the local mass in the repulsive case.  We also consider a supercritical super-Brownian motion. Again, it turns out that, conditioned on survival, its center of mass is a continuous process having an a.s. limit.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	National Security Agency
7.	Date	(YYYY-MM-DD)	2010-11-18
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/822
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-822
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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