EJP Reading Tools

On the Critical Point of the Random Walk Pinning Model in Dimension d=3

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On the Critical Point of the Random Walk Pinning Model in Dimension d=3
2.	Creator	Author's name, affiliation, country	Quentin Berger; ÉNS Lyon; France
2.	Creator	Author's name, affiliation, country	Fabio Toninelli; CNRS and ÉNS Lyon; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Pinning Models, Random Walk, Fractional Moment Method, Marginal Disorder
3.	Subject	Subject classification	82B44, 60K35, 82B27, 60K37
4.	Description	Abstract	We consider the Random Walk Pinning Model studied in [Birkner-Sun 2008] and [Birkner-Greven-den Hollander 2008]: this is a random walk $X$ on $\mathbb{Z}^d$, whose law is modified by the exponential of beta times the collision local time up to time $N$ with the (quenched) trajectory $Y$ of another $d$-dimensional random walk. If $\beta$ exceeds a certain critical value $\beta_c$, the two walks stick together for typical $Y$ realizations (localized phase). A natural question is whether the disorder is relevant or not, that is whether the quenched and annealed systems have the same critical behavior. Birkner and Sun proved that $\beta_c$ coincides with the critical point of the annealed Random Walk Pinning Model if the space dimension is $d=1$ or $d=2$, and that it differs from it in dimension $d$ larger or equal to $4$ (for $d$ strictly larger than $4$, the result was proven also in [Birkner-Greven-den Hollander 2008]). Here, we consider the open case of the marginal dimension $d=3$, and we prove non-coincidence of the critical points.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	This work was supported by the European Research Council through the ``Advanced Grant'' PTRELSS 228032, and by ANR through the grant LHMSHE
7.	Date	(YYYY-MM-DD)	2010-05-17
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/761
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-761
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
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.