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Intermittency on catalysts: symmetric exclusion

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Intermittency on catalysts: symmetric exclusion
2.	Creator	Author's name, affiliation, country	Jürgen Gärtner; Institut für Mathematik, Technische Universität Berlin
2.	Creator	Author's name, affiliation, country	Frank den Hollander; Mathematical Institute, Leiden University
2.	Creator	Author's name, affiliation, country	Gregory Maillard; Institut de Mathematiques, Ecole Polytechnique Federale de Lausanne
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Parabolic Anderson model; catalytic random medium; exclusion processes; Lyapunov exponents; intermittency
3.	Subject	Subject classification	Primary 60H25, 82C44; secondary 60F10, 35B40;
4.	Description	Abstract	We continue our study of intermittency for the parabolic Anderson equation, i.e., the spatially discrete heat equation on the d-dimensional integer lattice with a space-time random potential. The solution of the equation describes the evolution of a "reactant" under the influence of a "catalyst". In this paper we focus on the case where the random field is an exclusion process with a symmetric random walk transition kernel, starting from Bernoulli equilibrium. We consider the annealed Lyapunov exponents, i.e., the exponential growth rates of the successive moments of the solution. We show that these exponents are trivial when the random walk is recurrent, but display an interesting dependence on the diffusion constant when the random walk is transient, with qualitatively different behavior in different dimensions. Special attention is given to the asymptotics of the exponents when the diffusion constant tends to infinity, which is controlled by moderate deviations of the random field requiring a delicate expansion argument. In Gärtner and den Hollander [10] the case of a Poisson field of independent (simple) random walks was studied. The two cases show interesting differences and similarities. Throughout the paper, a comparison of the two cases plays a crucial role.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2007-05-01
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/407
10.	Identifier	Digital Object Identifier	10.1214/EJP.v12-407
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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