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Large deviations for non-crossing partitions


 
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1. Title Title of document Large deviations for non-crossing partitions
 
2. Creator Author's name, affiliation, country Janosch Ortmann; University of Warwick; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Large deviations; non-crossing partitions; free probability
 
3. Subject Subject classification 60F10; 46L54
 
4. Description Abstract We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. Using well-known bijections we relate this to other combinatorial objects, including Dyck paths, permutations and parking functions. As an application we obtain a variational formula for the maximum of the support of a compactly supported probability measure in terms of its free cumulants, provided these are all non negative. This is useful in free probability theory, where sometimes the R-transform is known but cannot be inverted explicitly to yield the density.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-05-06
 
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/2007
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2007
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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