Gaussian Multiplicative Chaos and KPZ Duality

被引：0
作者：
Julien Barral
Xiong Jin
Rémi Rhodes
Vincent Vargas
机构：
[1] Université Paris 13,
[2] Institut Galilée,undefined
[3] LAGA,undefined
[4] UMR CNRS 7539,undefined
[5] University of St Andrews,undefined
[6] Mathematics Institute,undefined
[7] North Haugh,undefined
[8] Université Paris-Dauphine,undefined
[9] Ceremade,undefined
[10] UMR 7534,undefined
[11] Place du maréchal de Lattre de Tassigny,undefined
来源：
Communications in Mathematical Physics | 2013年 / 323卷
关键词：
Hausdorff Dimension; Random Measure; Duality Relation; Poisson Random Measure; Covariance Kernel;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter γ2 beyond the transition phase (i.e. γ2 > 2d) and check the duality relation with sub-critical Gaussian multiplicative chaos. On the other hand, we give a simplified proof of the classical KPZ formula as well as the dual KPZ formula for atomic Gaussian multiplicative chaos. In particular, this framework allows to construct singular Liouville measures and to understand the duality relation in Liouville quantum gravity.
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页码：451 / 485
页数：34
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