Reconstructing the base field from imaginary multiplicative chaos
Abstract
We show that the imaginary multiplicative chaos $\exp(i\beta \Gamma)$ determines the gradient of the underlying field $\Gamma$ for all logcorrelated Gaussian fields with covariance of the form $\log xy + g(x,y)$ 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.05917
 arXiv:
 arXiv:2006.05917
 Bibcode:
 2020arXiv200605917A
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 60G15;
 60G20;
 60G57;
 60G60;
 82B21
 EPrint:
 Most notable changes in the title, unfortunately still no figures