Corpus ID: 220055909

# Reconstructing the base field from imaginary multiplicative chaos

@article{Aru2020ReconstructingTB,
title={Reconstructing the base field from imaginary multiplicative chaos},
author={Juhan Aru and Janne Junnila},
journal={arXiv: Probability},
year={2020}
}
• Published 2020
• Mathematics, Physics
• arXiv: Probability
• We show that the imaginary multiplicative chaos $\exp(i\beta \Gamma)$ determines the gradient of the underlying field $\Gamma$ for all log-correlated Gaussian fields with covariance of the form $-\log |x-y| + g(x,y)$ with mild regularity conditions on $g$, for all $d \geq 2$ and for all $\beta \in (0,\sqrt{d})$. In particular, we show that the 2D continuum zero boundary Gaussian free field is measurable w.r.t. its imaginary chaos.
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