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.
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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 : Thursday, July 18, 2019 - 3:00:04 PM
Long-term archiving on : Saturday, January 3, 2015 - 11:26:42 AM

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Nathanael Berestycki, Christophe Garban, Rémi Rhodes, Vincent Vargas. KPZ formula derived from Liouville heat kernel. Journal of the London Mathematical Society, London Mathematical Society, 2016, 94 (1), pp.186-208. ⟨http://onlinelibrary.wiley.com/doi/10.1112/jlms/jdw031/full#references⟩. ⟨hal-01071004⟩

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