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Subgaussian concentration and rates of convergence in directed polymers


 
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1. Title Title of document Subgaussian concentration and rates of convergence in directed polymers
 
2. Creator Author's name, affiliation, country Kenneth S. Alexander; University of Southern California; United States
 
2. Creator Author's name, affiliation, country Nikolaos Zygouras; University of Warwick; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) directed polymers, concentration, modified Poincar\'e inequalities, coarse graining
 
3. Subject Subject classification 82B44; 82D60; 60K35
 
4. Description Abstract We consider directed random polymers in $(d+1)$ dimensions with nearly gamma i.i.d. disorder.  We study the partition function $Z_{N,\omega}$ and establish exponential concentration of $\log Z_{N,\omega}$ about its mean on the subgaussian scale $\sqrt{N/\log N}$ . This is used to show that $\mathbb{E}[ \log Z_{N,\omega}]$ differs from $N$ times the free energy by an amount which is also subgaussian (i.e. $o(\sqrt{N})$), specifically $O( \sqrt{\frac{N}{\log N}}\log \log N)$
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF, European Council FP7
 
7. Date (YYYY-MM-DD) 2013-01-11
 
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/2005
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2005
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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