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arXiv · 1704.06058

Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation

Ellen Powell
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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.

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Ellen Powell. 2022-11-23. Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. https://doi.org/10.1214/18-ejp157

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