• Corpus ID: 247244552

What is a random surface?

@inproceedings{Sheffield2022WhatIA,
  title={What is a random surface?},
  author={Scott Sheffield},
  year={2022}
}
Given 2n unit equilateral triangles, there are finitely many ways to glue each edge to a partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the gluings that produce a topological sphere. As n → ∞ these random surfaces (appropriately scaled) converge in law. The limit is a “canonical” sphere-homeomorphic random surface, much the way Brownian motion is a canonical random path. Depending on how the surface space and convergence topology are specified, the limit is… 
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