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The limiting process of $N$-particle branching random walk with polynomial tails

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The limiting process of $N$-particle branching random walk with polynomial tails
2.	Creator	Author's name, affiliation, country	Jean Bérard; Université de Strasbourg; France
2.	Creator	Author's name, affiliation, country	Pascal Maillard; The Weizmann Institute of Science; Israel
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	branching random walk ; heavy-tailed distribution ; selection
3.	Subject	Subject classification	60K35 ; 60J80
4.	Description	Abstract	We consider a system of $N$ particles on the real line  that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the positive reals and 3) only the $N$ right most particles are retained, the others being removed from the system. This system has been introduced in the physics literature as an example of a microscopic stochastic model describing the propagation of a front. Its behavior for large $N$ is now well understood - both from a physical and mathematical viewpoint - in the case where the displacement distribution admits exponential moments. Here, we consider the case of displacements with regularly varying tails, where the relevant space and time scales are markedly different. We characterize the behavior of the system for two distinct asymptotic regimes. First, we prove convergence in law of the rescaled positions of the particles on a time scale of order $\log N$ and give a construction of the limit based on the records of a space time Poisson point process. Second, we determine the appropriate scaling when we let first the time horizon, then $N$ go to infinity.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-02-18
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/3111
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3111
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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