Electronic Journal of Probability

Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Ellen Powell

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 31, 26 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1522375271

Digital Object Identifier
doi:10.1214/18-EJP157

Mathematical Reviews number (MathSciNet)
MR3785401

Zentralblatt MATH identifier
1390.60182

Subjects
Primary: 60G57: Random measures 60G60: Random fields

Keywords
Gaussian multiplicative chaos random measures Liouville measure Gaussian free field

Rights
Creative Commons Attribution 4.0 International License.

Citation

Powell, Ellen. Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electron. J. Probab. 23 (2018), paper no. 31, 26 pp. doi:10.1214/18-EJP157. https://projecteuclid.org/euclid.ejp/1522375271


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