Open Access
2012 Large deviations for non-crossing partitions
Janosch Ortmann
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Electron. J. Probab. 17: 1-25 (2012). DOI: 10.1214/EJP.v17-2007


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.


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Janosch Ortmann. "Large deviations for non-crossing partitions." Electron. J. Probab. 17 1 - 25, 2012.


Accepted: 6 May 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1258.60028
MathSciNet: MR2924367
Digital Object Identifier: 10.1214/EJP.v17-2007

Primary: 60F10
Secondary: 46L54

Keywords: Free probability , large deviations , non-crossing partitions

Vol.17 • 2012
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