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On the Approach to Equilibrium for a Polymer with Adsorption and Repulsion

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On the Approach to Equilibrium for a Polymer with Adsorption and Repulsion
2.	Creator	Author's name, affiliation, country	Pietro Caputo; Universita Roma Tre
2.	Creator	Author's name, affiliation, country	Fabio Martinelli; Universita Roma Tre
2.	Creator	Author's name, affiliation, country	Fabio Lucio Toninelli; ENS Lyon
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Pinning model; Spectral gap; Mixing time; Coupling; Dynamical phase transition
3.	Subject	Subject classification	60K35; 82C20
4.	Description	Abstract	We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after $L$ steps, $L\in 2\mathbb{N}$. In the pinning model each path $\eta$ has a weight $\lambda^{N(\eta)}$, where $\lambda>0$ and $N(\eta)$ is the number of zeros in $\eta$. When the paths are constrained to be non--negative, the polymer is said to satisfy a hard--wall constraint. Such models are well known to undergo a localization/delocalization transition as the pinning strength $\lambda$ is varied. In this paper we study a natural ``spin flip'' dynamics for %associated to these models and derive several estimates on its spectral gap and mixing time. In particular, for the system with the wall we prove that relaxation to equilibrium is always at least as fast as in the free case (\ie $\lambda=1$ without the wall), where the gap and the mixing time are known to scale as $L^{-2}$ and $L^2\log L$, respectively. This improves considerably over previously known results. For the system without the wall we show that the equilibrium phase transition has a clear dynamical manifestation: for $\lambda\geq 1$ relaxation is again at least as fast as the diffusive free case, but in the strictly delocalized phase ($\lambda<1$) the gap is shown to be $O(L^{-5/2})$, up to logarithmic corrections. As an application of our bounds, we prove stretched exponential relaxation of local functions in the localized regime.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2008-02-22
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/486
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-486
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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