arXiv:1512.06190 Abstract | arXiv Analytics

arXiv:1512.06190 [math.PR]Abstract References Reviews Resources

Two perspectives of the unit area quantum sphere and their equivalence

Published 2015-12-19Version 1

Recently David, Kupiainen, Rhodes, Vargas (2014) and Duplantier, Miller, Sheffield (2014) provided two different probabilistic perspectives on Liouville quantum gravity on the sphere. In particular, in each of them one may find a definition of the unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.

Comments: 25 pages

Categories: math.PR, math-ph, math.MP

Subjects: 60D05, 81T40, 81T20

Keywords: equivalence, respective unit area quantum spheres, liouville quantum gravity, probabilistic perspectives

Related articles: Most relevant | Search more

arXiv:1504.00625 [math.PR] (Published 2015-04-02)

Liouville Quantum Gravity on the complex tori

François David, Rémi Rhodes, Vincent Vargas

arXiv:1410.7318 [math.PR] (Published 2014-10-27)

Liouville Quantum Gravity on the Riemann sphere

François David, Antti Kupiainen, Rémi Rhodes, Vincent Vargas

arXiv:1506.01968 [math.PR] (Published 2015-06-05)