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Competing Particle Systems Evolving by I.I.D. Increments

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Competing Particle Systems Evolving by I.I.D. Increments
2.	Creator	Author's name, affiliation, country	Mykhaylo Shkolnikov; Stanford University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Competing particle systems, Large deviations, Spin glasses
3.	Subject	Subject classification	60G55, 60G70, 60K40, 62P35
4.	Description	Abstract	We consider competing particle systems in $\mathbb{R}^d$, i.e. random locally finite upper bounded configurations of points in $\mathbb{R}^d$ evolving in discrete time steps. In each step i.i.d. increments are added to the particles independently of the initial configuration and the previous steps. Ruzmaikina and Aizenman characterized quasi-stationary measures of such an evolution, i.e. point processes for which the joint distribution of the gaps between the particles is invariant under the evolution, in case $d=1$ and restricting to increments having a density and an everywhere finite moment generating function. We prove corresponding versions of their theorem in dimension $d=1$ for heavy-tailed increments in the domain of attraction of a stable law and in dimension $d\geq 1$ for lattice type increments with an everywhere finite moment generating function. In all cases we only assume that under the initial configuration no two particles are located at the same point. In addition, we analyze the attractivity of quasi-stationary Poisson point processes in the space of all Poisson point processes with almost surely infinite, locally finite and upper bounded configurations.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF
7.	Date	(YYYY-MM-DD)	2009-03-11
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/635
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-635
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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