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Correlation Lengths for Random Polymer Models and for Some Renewal Sequences


 
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1. Title Title of document Correlation Lengths for Random Polymer Models and for Some Renewal Sequences
 
2. Creator Author's name, affiliation, country Fabio Lucio Toninelli; ENS LYON
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Pinning and Wetting Models, Typical and Average Correlation Lengths, Critical Exponents, Renewal Theory, Exponential Convergence Rates
 
3. Subject Subject classification 82B27, 82B44, 82B41, 60K05
 
4. Description Abstract We consider models of directed polymers interacting with a one-dimensional defect line on which random charges are placed. More abstractly, one starts from renewal sequence on $Z$ and gives a random (site-dependent) reward or penalty to the occurrence of a renewal at any given point of $Z$. These models are known to undergo a delocalization-localization transition, and the free energy $F$ vanishes when the critical point is approached from the localized region. We prove that the quenched correlation length $\xi$, defined as the inverse of the rate of exponential decay of the two-point function, does not diverge faster than $1/F$. We prove also an exponentially decaying upper bound for the disorder-averaged two-point function, with a good control of the sub-exponential prefactor. We discuss how, in the particular case where disorder is absent, this result can be seen as a refinement of the classical renewal theorem, for a specific class of renewal sequences.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) GIP-ANR project JC05 42461 POLINTBIO
 
7. Date (YYYY-MM-DD) 2007-05-13
 
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/414
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-414
 
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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