All Outputs (4)

Lecture notes on the Gaussian free field (2021)
Book
Werner, W., & Powell, E. (2021). Lecture notes on the Gaussian free field. Société Mathématique de France

The Gaussian Free Field (GFF) in the continuum appears to be the natural generalisation of Brownian motion, when one replaces time by a multidimensional continuous parameter. While Brownian motion can be viewed as the most natural random real-valued... Read More about Lecture notes on the Gaussian free field.

Critical Gaussian multiplicative chaos: a review (2021)
Journal Article
Powell, E. (2021). Critical Gaussian multiplicative chaos: a review. Markov processes and related fields, 27(4), 557-606

This review-style article presents an overview of recent progress in constructing and studying critical Gaussian multiplicative chaos. A proof that the critical measure in any dimension can be obtained as a limit of subcritical measures is given.

Conformal welding for critical Liouville quantum gravity (2021)
Journal Article
Holden, N., & Powell, E. (2021). Conformal welding for critical Liouville quantum gravity. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 57(3), 1229-1254. https://doi.org/10.1214/20-aihp1116

Consider two critical Liouville quantum gravity surfaces (i.e., γ-LQG for γ = 2), each with the topology of H and with infinite boundary length. We prove that there a.s. exists a conformal welding of the two surfaces, when the boundaries are identifi... Read More about Conformal welding for critical Liouville quantum gravity.

(1+𝜀) moments suffice to characterise the GFF (2021)
Journal Article
Berestycki, N., Powell, E., & Ray, G. (2021). (1+𝜀) moments suffice to characterise the GFF. Electronic Journal of Probability, 26(44), 1-25. https://doi.org/10.1214/20-ejp566

We show that there is “no stable free field of index α ∈ ( 1 , 2 ) ”, in the following sense. It was proved in [4] that subject to a fourth moment assumption, any random generalised function on a domain D of the plane, satisfying conformal invariance... Read More about (1+𝜀) moments suffice to characterise the GFF.