The distance-dependent two-point function of triangulations: a new derivation from old results
Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 2, pp. 177-211.

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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/38
Classification : 05-XX
Mots-clés : Planar maps, triangulations, two-point function, hull 
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     author = {Guitter, Emmanuel},
     title = {The distance-dependent two-point function of triangulations: a new derivation from old results},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {177--211},
     volume = {4},
     number = {2},
     year = {2017},
     doi = {10.4171/aihpd/38},
     zbl = {1379.05029},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/38/}
}
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Guitter, Emmanuel. The distance-dependent two-point function of triangulations: a new derivation from old results. Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 2, pp. 177-211. doi : 10.4171/aihpd/38. http://archive.numdam.org/articles/10.4171/aihpd/38/

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