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Appears in collection : Random Geometry / Géométrie aléatoire

In this talk, based on joint work with Alexandre Stauffer, I will consider the problem of providing 'uniform growth schemes' for various types of planar maps. In particular, we will discuss how to couple a uniform map with n faces with a uniform map with n+1 faces in such a way that the smaller map is always obtained from the larger by collapsing a single face. We show that uniform growth schemes exist for rooted 2p-angulations of the sphere and for rooted simple triangulations.

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Bibliography

  • CARACENI, Alessandra et STAUFFER, Alexandre. Growing uniform planar maps face by face. arXiv preprint arXiv:2110.14575, 2021. - https://arxiv.org/abs/2110.14575
  • CARACENI, Alessandra. A polynomial upper bound for the mixing time of edge rotations on planar maps. Electronic Journal of Probability, 2020, vol. 25, p. 1-30. - http://dx.doi.org/10.1214/20-EJP519

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