14th Northwest Probability Seminar – Recurrence of planar graph limits.

  • Asaf Nachmias | University of British Columbia

We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite planar triangulation and quadrangulation (UIPT and UIPQ) are almost surely recurrent, resolving a conjecture of Angel, Benjamini and Schramm.

Joint work with Ori Gurel-Gurevich.

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