English

Gaussian multiplicative chaos and KPZ duality

Probability 2015-06-04 v4 Mathematical Physics math.MP

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 γ2\gamma^2 beyond the transition phase (i.e. γ2>2d\gamma^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.

Cite

@article{arxiv.1202.5296,
  title  = {Gaussian multiplicative chaos and KPZ duality},
  author = {Julien Barral and Xiong Jin and Rémi Rhodes and Vincent Vargas},
  journal= {arXiv preprint arXiv:1202.5296},
  year   = {2015}
}

Comments

Typo fixed in the title. To appear in Communications in Mathematical Physics

R2 v1 2026-06-21T20:24:15.287Z