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Article Dans Une Revue Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions Année : 2017

The distance-dependent two-point function of triangulations: a new derivation from old results

Résumé

We present a new derivation of the distance-dependent two-point function of random planar triangulations. As it is well-known, this function is intimately related to the generating functions of so-called slices, which are pieces of triangulation having boundaries made of shortest paths of prescribed length. We show that the slice generating functions are fully determined by a direct recursive relation on their boundary length. Remarkably, the kernel of this recursion is some quantity introduced and computed by Tutte a long time ago in the context of a global enumeration of planar triangulations. We may thus rely on these old results to solve our new recursion relation explicitly in a constructive way.
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Dates et versions

hal-01236866 , version 1 (25-02-2016)

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Emmanuel Guitter. The distance-dependent two-point function of triangulations: a new derivation from old results. Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2017, 4, pp.177-211. ⟨10.4171/AIHPD/38⟩. ⟨hal-01236866⟩
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