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Gaussian multiplicative chaos and applications: A review

In this article, we review the theory of Gaussian multiplicative chaos initially introduced by Kahane’s seminal work in 1985. Though this beautiful paper faded from memory until recently, it already… Expand

Liouville Quantum Gravity on the Riemann Sphere

- F. David, A. Kupiainen, R. Rhodes, V. Vargas
- Mathematics
- 27 October 2014

In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like… Expand

Complex Gaussian Multiplicative Chaos

In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all… Expand

Integrability of Liouville theory: proof of the DOZZ formula

- A. Kupiainen, R. Rhodes, V. Vargas
- MathematicsAnnals of Mathematics
- 27 July 2017

Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996) proposed a remarkable explicit expression, the so-called DOZZ formula, for the 3 point structure constants of Liouville… Expand

Critical Gaussian multiplicative chaos: Convergence of the derivative martingale

- B. Duplantier, R. Rhodes, S. Sheffield, V. Vargas
- Mathematics
- 8 June 2012

In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching… Expand

Liouville Brownian motion

We construct a stochastic process, called the Liouville Brownian motion which we conjecture to be the scaling limit of random walks on large planar maps which are embedded in the euclidean plane or… Expand

Liouville quantum gravity on complex tori

In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the… Expand

KPZ formula for log-infinitely divisible multifractal random measures

We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. Comm. Math. Phys. 236 (2003) 449–475]. If M is a non degenerate… Expand

Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation

- B. Duplantier, R. Rhodes, S. Sheffield, V. Vargas
- Mathematics
- 4 April 2014

Gaussian Multiplicative Chaos is a way to produce a measure on $${\mathbb{R}^d}$$Rd (or subdomain of $${\mathbb{R}^d}$$Rd) of the form $${e^{\gamma X(x)} dx}$$eγX(x)dx, where X is a log-correlated… Expand

Gaussian Multiplicative Chaos and KPZ Duality

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… Expand

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