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KPZ formula derived from Liouville heat kernel
Abstract : In this paper, we establish the Knizhnik--Polyakov--Zamolodchikov (KPZ) formula of Liouville quantum gravity, using the heat kernel of Liouville Brownian motion. This derivation of the KPZ formula was first suggested by F. David and M. Bauer in order to get a geometrically more intrinsic way of measuring the dimension of sets in Liouville quantum gravity. We also provide a careful study of the (no)-doubling behaviour of the Liouville measures in the appendix, which is of independent interest.
https://hal-upec-upem.archives-ouvertes.fr/hal-01071004
Contributor : Rémi Rhodes <>
Submitted on : Thursday, October 2, 2014 - 8:26:42 PM
Last modification on : Tuesday, December 8, 2020 - 10:50:27 AM
Long-term archiving on: : Saturday, January 3, 2015 - 11:26:42 AM
Contributor : Rémi Rhodes <>
Submitted on : Thursday, October 2, 2014 - 8:26:42 PM
Last modification on : Tuesday, December 8, 2020 - 10:50:27 AM
Long-term archiving on: : Saturday, January 3, 2015 - 11:26:42 AM
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