Reconstructing the base field from imaginary multiplicative chaos

25/6/20 Published in : arXiv:2006.05917

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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