Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Open access
Author
Date
2018Type
- Journal Article
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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000267611Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsSubject
Gaussian multiplicative chaos; random measures; Liouville measure; Gaussian free fieldOrganisational unit
09453 - Werner, Wendelin / Werner, Wendelin
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