Asymptotic expansion of the multi-orientable random tensor model

Eric Fusy (1) , Adrian Tanasa (2, 3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 Horia Hulubei National Institute for Physics and Nuclear Engineering
3 LIPN - Laboratoire d'Informatique de Paris-Nord

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expansion in N , the size of the tensor, of a particular random ten-sor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.

Mots clés: 3D maps; 4-regular maps; Eulerian orientations; schemes

Domaines: Combinatoire [math.CO]

Eric Fusy, Adrian Tanasa. Asymptotic expansion of the multi-orientable random tensor model. The Electronic Journal of Combinatorics, 2015, 22 (1), pp.P1.52. ⟨hal-01188329⟩