An elementary approach to Gaussian multiplicative chaos
Open Access
- 1 January 2017
- journal article
- Published by Institute of Mathematical Statistics in Electronic Communications in Probability
- Vol. 22 (none)
- https://doi.org/10.1214/17-ecp58
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).
Keywords
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