123 citations · 404 across the 40 of their papers we have counts for
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The diameter of uniform spanning trees in high dimensions
Peleg Michaeli, Asaf Nachmias, Matan Shalev
We show that the diameter of a uniformly drawn spanning tree of a connected graph on vertices which satisfies certain high-dimensionality conditions typically grows like $Θ(\sq…
The Dirichlet problem for orthodiagonal maps
Ori Gurel-Gurevich, Daniel C. Jerison, Asaf Nachmias
We prove that the discrete harmonic function corresponding to smooth Dirichlet boundary conditions on orthodiagonal maps, that is, plane graphs having quadrilateral faces with orth…
A combinatorial criterion for macroscopic circles in planar triangulations
Ori Gurel-Gurevich, Daniel C. Jerison, Asaf Nachmias
Given a finite simple triangulation, we estimate the sizes of circles in its circle packing in terms of Cannon's vertex extremal length. Our estimates provide control over the size…
Planar maps, random walks and circle packing
Asaf Nachmias
These are lecture notes of the 48th Saint-Flour summer school, July 2018, on the topic of planar maps, random walks and the circle packing theorem.