Large Deviations for Non-Crossing Partitions
Probability
2011-07-04 v1
Abstract
We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. 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.
Cite
@article{arxiv.1107.0208,
title = {Large Deviations for Non-Crossing Partitions},
author = {Janosch Ortmann},
journal= {arXiv preprint arXiv:1107.0208},
year = {2011}
}