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Collision Local Time of Transient Random Walks and Intermediate Phases in Interacting Stochastic Systems

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Collision Local Time of Transient Random Walks and Intermediate Phases in Interacting Stochastic Systems
2.	Creator	Author's name, affiliation, country	Matthias Birkner; University Mainz; Germany
2.	Creator	Author's name, affiliation, country	Andreas Greven; Universität Erlangen Nürnberg; Germany
2.	Creator	Author's name, affiliation, country	Frank den Hollander; Leiden University and Eurandom; Netherlands
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random walks, collision local time, annealed vs. quenched, large deviation principle, interacting stochastic systems, intermediate phase
3.	Subject	Subject classification	60G50, 60F10, 60K35, 82D60
4.	Description	Abstract	In a companion paper (M. Birkner, A. Greven, F. den Hollander, Quenched LDP for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403-456), a quenched large deviation principle (LDP) has been established for the empirical process of words obtained by cutting an i.i.d. sequence of letters into words according to a renewal process. We apply this LDP to prove that the radius of convergence of the generating function of the collision local time of two independent copies of a symmetric and strongly transient random walk on $\mathbb{Z}^d$, $d\geq1$, both starting from the origin, strictly increases when we condition on one of the random walks, both in discrete time and in continuous time. We conjecture that the same holds when the random walk is transient but not strongly transient. The presence of these gaps implies the existence of an intermediate phase for the long-time behaviour of a class of coupled branching processes, interacting diffusions, respectively, directed polymers in random environments.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Dutch-German Bilateral Research Group ``Mathematics of Random Spatial Models from Physics and Biology''
7.	Date	(YYYY-MM-DD)	2011-01-11
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/878
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-878
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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