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Moment asymptotics for branching random walks in random environment

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Moment asymptotics for branching random walks in random environment
2.	Creator	Author's name, affiliation, country	Wolfgang König; Weierstrass Institute Berlin and TU Berlin; Germany
2.	Creator	Author's name, affiliation, country	Onur Gün; Weirstrass Institute Berlin
2.	Creator	Author's name, affiliation, country	Ozren Sekulović; Freie Universität Berlin
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	branching random walk, random potential, parabolic Anderson model, Feynman-Kac-type formula, annealed moments, large deviations
3.	Subject	Subject classification	60J80, 60J55, 60F10, 60K37
4.	Description	Abstract	We consider the long-time behaviour of a branching random walk in random environment on the lattice  $\mathbb{Z}^d$. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random potential of spatially dependent killing/branching rates. The main objects of our interest are the annealed moments $\langle m_n^p \rangle $, i.e., the  $p$-th moments over the medium of the $n$-th moment over the migration and killing/branching, of the local and global population sizes. For $n=1$, this is well-understood, as $m_1$ is closely connected with the parabolic Anderson model. For some special distributions, this was extended to $n\geq2$, but only as to the first term of the asymptotics, using (a recursive version of) a Feynman-Kac formula for $m_n$. In this work we derive also the second term of the asymptotics, for a much larger class of distributions. In particular, we show that $\langle m_n^p \rangle$ and $\langle m_1^{np} \rangle$ are asymptotically equal, up to an error $\e^{o(t)}$. The cornerstone of our method is a direct Feynman-Kac type formula for $m_n$, which we establish using known spine techniques.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-06-21
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/2212
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2212
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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