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Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Powell, Ellen

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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 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
Public URL https://durham-repository.worktribe.com/output/1290330

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