Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Powell, Ellen

doi:10.1214/18-ejp157

Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Powell, Ellen

Authors

Dr Ellen Powell ellen.g.powell@durham.ac.uk
Associate Professor

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