Borel transformations of random fields

In working with the Gaussian Multiplicative Chaos, one encounters various families of Borel transformations of random fields — such as, for instance , the normalized exponential or the truncated normalized exponential used by Nathanael Berestycki. The main result of this talk gives sufficient conditions ensuring the continuity in distribution for Borel transformations of random fields. The talk is based on the paper , “Continuity in distribution for Borel transformations of random fields”, Theory of prob. and appl.., 70:4 (2025), 663–671