EJP Reading Tools

Intermittency on catalysts: three-dimensional simple symmetric exclusion

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Intermittency on catalysts: three-dimensional simple 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	Grégory Maillard; CMI-LATP, Université de Provence
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Parabolic Anderson model; catalytic random medium; exclusion process; graphical representation; Lyapunov exponents; intermittency; large deviations
3.	Subject	Subject classification	Primary 60H25, 82C44; Secondary 60F10, 35B40.
4.	Description	Abstract	We continue our study of intermittency for the parabolic Anderson model $\partial u/\partial t = \kappa\Delta u + \xi u$ in a space-time random medium $\xi$, where $\kappa$ is a positive diffusion constant, $\Delta$ is the lattice Laplacian on $\mathbb{Z}^d$, $d \geq 1$, and $\xi$ is a simple symmetric exclusion process on $\mathbb{Z}^d$ in Bernoulli equilibrium. This model describes the evolution of a reactant $u$ under the influence of a catalyst $\xi$. In Gärtner, den Hollander and Maillard [3] we investigated the behavior of the annealed Lyapunov exponents, i.e., the exponential growth rates as $t\to\infty$ of the successive moments of the solution $u$. This led to an almost complete picture of intermittency as a function of $d$ and $\kappa$. In the present paper we finish our study by focussing on the asymptotics of the Lyaponov exponents as $\kappa\to\infty$ in the critical dimension $d=3$, which was left open in Gärtner, den Hollander and Maillard [3] and which is the most challenging. We show that, interestingly, this asymptotics is characterized not only by a Green term, as in $d\geq 4$, but also by a polaron term. The presence of the latter implies intermittency of all orders above a finite threshold for $\kappa$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2009-09-28
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/694
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-694
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.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.