Large deviations for non-crossing partitions

Stochastic Analysis Seminar Series

We establish a large deviations principle for the block sizes of a uniformly random 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.

Location:
Speaker(s):

Janosch Ortmann (University of Warwick)

Date:
Monday, October 17, 2011 - 14:15
to 15:15