Critical Liouville measure as a limit of subcritical measures

We study how the Gaussian multiplicative chaos (GMC) measures $μ^γ$ corresponding to the 2D Gaussian free field change when $γ$ approaches the critical parameter $2$. In particular, we show that as $γ\to 2^{-}$, $(2-γ)^{-1}μ^γ$ converges in probability to $2μ'$, where $μ'$ is the critical GMC measure.

No reviews yet.

No comments yet.