On the Riemann surface type of random planar maps | Zendy

James T. Gill | Zendy; Steffen Rohde | Zendy

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On the Riemann surface type of random planar maps

Author(s) -

James T. Gill,

Steffen Rohde

Publication year - 2013

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/749

Subject(s) - planar , type (biology) , riemann surface , mathematics , surface (topology) , geometry , mathematical analysis , computer science , geology , computer graphics (images) , paleontology

We show that the (random) Riemann surfaces of the Angel-Schramm Uniform Infinite Planar Triangulation and of Sheffield's infinite necklace construction are both parabolic. In other words, Brownian motion on these surfaces is recurrent. We obtain this result as a corollary to a more general theorem on subsequential distributional limits of random unbiased disc triangulations, following work of Benjamini and Schramm.

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