Document Zbl 1365.60035

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An elementary approach to Gaussian multiplicative chaos. (English) Zbl 1365.60035

Electron. Commun. Probab. 22, Paper No. 27, 12 p. (2017).

Summary: 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).

Cited in 1 Review

Cited in 116 Documents

MSC:

60G15	Gaussian processes
60G60	Random fields
60F99	Limit theorems in probability theory
60G57	Random measures
60K37	Processes in random environments
60J67	Stochastic (Schramm-)Loewner evolution (SLE)
60J65	Brownian motion

Keywords:

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

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