Electronic Communications in Probability

An elementary approach to Gaussian multiplicative chaos

Nathanaël Berestycki

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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

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

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

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Zentralblatt MATH identifier

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

Gaussian multiplicative chaos Gaussian free field thick points Liouville quantum gravity

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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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