Gaussian Multiplicative Chaos and KPZ Duality

Julien Barral; Xiong Jin; Rémi Rhodes; Vincent Vargas

doi:10.1007/s00220-013-1769-z

Gaussian Multiplicative Chaos and KPZ Duality

Julien Barral, Xiong Jin, Rémi Rhodes, Vincent Vargas

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Abstract

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 γ 2 beyond the transition phase (i.e. γ 2 > 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. © 2013 Springer-Verlag Berlin Heidelberg.

Original language	English
Pages (from-to)	451-485
Number of pages	34
Journal	Communications in Mathematical Physics
Volume	323
Issue number	2
DOIs	https://doi.org/10.1007/s00220-013-1769-z
Publication status	Published - Oct 2013

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title = "Gaussian Multiplicative Chaos and KPZ Duality",

abstract = "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 γ 2 beyond the transition phase (i.e. γ 2 > 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. {\textcopyright} 2013 Springer-Verlag Berlin Heidelberg.",

author = "Julien Barral and Xiong Jin and R{\'e}mi Rhodes and Vincent Vargas",

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T1 - Gaussian Multiplicative Chaos and KPZ Duality

AU - Barral, Julien

AU - Jin, Xiong

AU - Rhodes, Rémi

AU - Vargas, Vincent

PY - 2013/10

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N2 - 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 γ 2 beyond the transition phase (i.e. γ 2 > 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. © 2013 Springer-Verlag Berlin Heidelberg.

AB - 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 γ 2 beyond the transition phase (i.e. γ 2 > 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. © 2013 Springer-Verlag Berlin Heidelberg.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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Gaussian Multiplicative Chaos and KPZ Duality

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