Abstract:
We introduce a plane tree model, where each edge of the tree is equipped with a non-negative thickness parameter. This collection of trees, which is new to our knowledge, exhibits a simple yet rich recursive decomposition, giving rise to a Wiener-Hopf factorization for the generating functions. We are then able to solve this functional equation analytically via a Lagrangean parametrization. Furthermore, this tree model can be applied to the O(n) loop model on random planar maps, which is briefly explained during the talk. Based on a joint ongoing work with Jérémie Bouttier (Sorbonne Université) and Grégory Miermont (ENS de Lyon).