Open Access
2018 Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation
Ellen Powell
Electron. J. Probab. 23: 1-26 (2018). DOI: 10.1214/18-EJP157


We show that, for general convolution approximations to a large class of log-correlated fields, including the 2d Gaussian free field, the critical chaos measures with derivative normalisation converge to a limiting measure $\mu '$. This limiting measure does not depend on the choice of approximation. Moreover, it is equal to the measure obtained using the Seneta–Heyde renormalisation at criticality, or using a white-noise approximation to the field.


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Ellen Powell. "Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation." Electron. J. Probab. 23 1 - 26, 2018.


Received: 10 October 2017; Accepted: 12 March 2018; Published: 2018
First available in Project Euclid: 30 March 2018

zbMATH: 1390.60182
MathSciNet: MR3785401
Digital Object Identifier: 10.1214/18-EJP157

Primary: 60G57 , 60G60

Keywords: Gaussian free field , Gaussian multiplicative chaos , Liouville measure , Random measures

Vol.23 • 2018
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