Subcritical phase of complex Gaussian multiplicative chaos

Determine the limiting behavior of complex Gaussian multiplicative chaos in the phase P_2, the only phase of the complex Gaussian-multiplicative-chaos phase diagram that remains unresolved.

Background

The paper summarizes existing results for complex Gaussian multiplicative chaos in phases P_1 and P_3 and on the relevant phase boundaries. It explicitly identifies phase P_2 as untreated, making its limiting behavior an open problem.

References

Thus, only phase $P_2$ remains open.

— Fluctuations of additive martingale limits of branching Brownian motion  (2609.10530 - Chen et al., 9 Sep 2026) in Section 3, “Related literature and further questions,” paragraph “Gaussian multiplicative chaos”