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).
Citation
Nathanaël Berestycki. "An elementary approach to Gaussian multiplicative chaos." Electron. Commun. Probab. 22 1 - 12, 2017. https://doi.org/10.1214/17-ECP58
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