Electronic Communications in Probability

An elementary approach to Gaussian multiplicative chaos

Nathanaël Berestycki

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Abstract

A completely elementary and self-contained proof of convergence of Gaussian multiplicative chaos is given. The argument shows further that the limiting random measure is nontrivial in the entire subcritical phase $(\gamma < \sqrt{2d} )$ and that the limit is universal (i.e., the limiting measure is independent of the regularisation of the underlying field).

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 27, 12 pp.

Dates
Received: 25 May 2016
Accepted: 8 May 2017
First available in Project Euclid: 12 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1494554429

Digital Object Identifier
doi:10.1214/17-ECP58

Mathematical Reviews number (MathSciNet)
MR3652040

Zentralblatt MATH identifier
1365.60035

Subjects
Primary: 60K37: Processes in random environments 60J67: Stochastic (Schramm-)Loewner evolution (SLE) 60J65: Brownian motion [See also 58J65]

Keywords
Gaussian multiplicative chaos Gaussian free field thick points Liouville quantum gravity

Rights
Creative Commons Attribution 4.0 International License.

Citation

Berestycki, Nathanaël. An elementary approach to Gaussian multiplicative chaos. Electron. Commun. Probab. 22 (2017), paper no. 27, 12 pp. doi:10.1214/17-ECP58. https://projecteuclid.org/euclid.ecp/1494554429


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References

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