• Corpus ID: 119273169

# Nesting statistics in the $O(n)$ loop model on random planar maps

@article{Borot2016NestingSI,
title={Nesting statistics in the \$O(n)\$ loop model on random planar maps},
author={Gaetan Borot and J{\'e}r{\'e}mie Bouttier and Bertrand Duplantier},
journal={arXiv: Mathematical Physics},
year={2016}
}
• Published 7 May 2016
• Mathematics
• arXiv: Mathematical Physics
In the O(n) loop model on random planar maps, we study the depth – in terms of the number of levels of nesting – of the loop configuration, by means of analytic combinatorics. We focus on the " refined " generating series of pointed disks or cylinders, which keep track of the number of loops separating the marked point from the boundary (for disks), or the two boundaries (for cylinders). For the general O(n) loop model, we show that these generating series satisfy functional relations obtained…

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We pursue the analysis of nesting statistics in the $O(n)$ loop model on random maps, initiated for maps with the topology of disks and cylinders in math-ph/1605.02239, here for arbitrary topologies.
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