Electronic Journal of Probability
- Electron. J. Probab.
- Volume 23 (2018), paper no. 31, 26 pp.
Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation
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.
Electron. J. Probab., Volume 23 (2018), paper no. 31, 26 pp.
Received: 10 October 2017
Accepted: 12 March 2018
First available in Project Euclid: 30 March 2018
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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