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Large deviations for non-crossing partitions

   
@article{EJP2007,
	author = {Janosch Ortmann},
	title = {Large deviations for non-crossing partitions},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Large deviations; non-crossing partitions; free probability},
	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.},
	pages = {no. 34, 1-25},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-2007},    
        url = {http://ejp.ejpecp.org/article/view/2007}}