# Reconstructing the base field from imaginary multiplicative chaos

Juhan Aru, Janne Junnila

Juhan Aru, Janne Junnila

**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.