A Liouville quantum sphere is a random quantum surface with spherical topology, represented by a field and its Liouville quantum gravity area measure modulo conformal changes of coordinate. The unit-area version has total quantum area 1. Three independent points sampled from the quantum-area measure can be used to fix conformal coordinates on the unmarked unit-area surface.
Liouville Quantum Sphere
See also
Conformal Loop Ensemble, Fortuin-Kasteleyn Planar Map, Gaussian Multiplicative Chaos, Liouville Quantum GravityExplore with Wolfram|Alpha
References
Duplantier, B.; Miller, J.; and Sheffield, S. Liouville Quantum Gravity as a Mating of Trees. Paris, France: Société Mathématique de France, 2021. https://doi.org/10.24033/ast.1149.Cite this as:
Weisstein, Eric W. "Liouville Quantum Sphere." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LiouvilleQuantumSphere.html