Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Powell, Ellen

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 µ 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.

Citation

Powell, E. (2018). Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electronic Journal of Probability, 23, 1-26. https://doi.org/10.1214/18-ejp157

• Journal Article Type: Article
• Acceptance Date: Mar 12, 2018
• Online Publication Date: Mar 30, 2018
• Publication Date: Mar 30, 2018
• Deposit Date: Sep 28, 2019
• Publicly Available Date: Oct 8, 2019
• Journal: Electronic Journal of Probability
• Publisher: Institute of Mathematical Statistics
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Article Number: 31
• Pages: 1-26
• DOI: https://doi.org/10.1214/18-ejp157