The Tutte Embedding of the Poisson–Voronoi Tessellation of the Brownian Disk Converges to $$\sqrt{8/3}$$-Liouville Quantum Gravity
The Tutte Embedding of the Poisson–Voronoi Tessellation of the Brownian Disk Converges to $$\sqrt{8/3}$$-Liouville Quantum Gravity
Abstract Recent works have shown that an instance of a Brownian surface (such as the Brownian map or Brownian disk) a.s. has a canonical conformal structure under which it is equivalent to a $$\sqrt{8/3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mrow><mml:mn>8</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msqrt></mml:math> -Liouville quantum gravity (LQG) surface. In particular, Brownian motion on a Brownian surface is …