Fyodorov–Keating multiplicative-chaos conjecture for zeta-function densities

Let $T\to\fty$, let $\beta\in(0,2)$, and consider the random densities on $[0,1]$ given by

$$(\log T)^{-\frac{1}{4}\beta^2}\lvert\zeta(1/2+ix+iT)\rvert^\beta,\qquad x\in[0,1].$$

Multiplicative-chaos conjecture. These random densities should converge in distribution to a constant multiple of the multiplicative-chaos measure described in the source's Theorem. This conjecture proposes a precise link between the statistical behavior of the zeta function and real multiplicative chaos. The source notes that the required moment and correlation asymptotics remain out of reach.