Gaussian Multiplicative Chaos and KPZ Duality

Julien Barral, Xiong Jin, Rémi Rhodes, Vincent Vargas

    Research output: Contribution to journalArticlepeer-review


    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 languageEnglish
    Pages (from-to)451-485
    Number of pages34
    JournalCommunications in Mathematical Physics
    Issue number2
    Publication statusPublished - Oct 2013


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