Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Liouville heat kernel: Regularity and bounds

P. Maillard, R. Rhodes, V. Vargas, and O. Zeitouni

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We initiate in this paper the study of analytic properties of the Liouville heat kernel. In particular, we establish regularity estimates on the heat kernel and derive non-trivial lower and upper bounds.


Dans ce papier, nous initions l’étude des propriétés analytiques du noyau de la chaleur de Liouville. En particulier, nous établissons des estimées de régularité pour le noyau et nous l’encadrons par des bornes inférieures et supérieures non triviales.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 3 (2016), 1281-1320.

Received: 12 July 2014
Revised: 1 March 2015
Accepted: 22 March 2015
First available in Project Euclid: 28 July 2016

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Zentralblatt MATH identifier

Primary: 35K08: Heat kernel 60J60: Diffusion processes [See also 58J65] 60K37: Processes in random environments 60J55: Local time and additive functionals 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

Liouville quantum gravity Heat kernel Liouville Brownian motion Gaussian multiplicative chaos


Maillard, P.; Rhodes, R.; Vargas, V.; Zeitouni, O. Liouville heat kernel: Regularity and bounds. Ann. Inst. H. Poincaré Probab. Statist. 52 (2016), no. 3, 1281--1320. doi:10.1214/15-AIHP676.

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