All Outputs (2)

A characterisation of the Gaussian free field (2019)
Journal Article
Berestycki, N., Powell, E., & Ray, G. (2020). A characterisation of the Gaussian free field. Probability Theory and Related Fields, 176(3-4), 1259-1301. https://doi.org/10.1007/s00440-019-00939-9

We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.

Critical Liouville measure as a limit of subcritical measures (2019)
Journal Article
Aru, J., Powell, E., & Sepúlveda, A. (2019). Critical Liouville measure as a limit of subcritical measures. Electronic Communications in Probability, 24, 1-16. https://doi.org/10.1214/19-ecp209

We study how the Gaussian multiplicative chaos (GMC) measures μγ corresponding to the 2D Gaussian free field change when γ approaches the critical parameter 2. In particular, we show that as γ→2−, (2−γ)−1μγ converges in probability to 2μ′, where μ′ i... Read More about Critical Liouville measure as a limit of subcritical measures.