Staff profile

Research Interests

My research involves, broadly, the study of random systems at criticality. I am particularly interested in critical phenomena, scaling limits and more generally, random geometry. This is the study of the random curves and surfaces which arise as scaling limits of critical statistical physics models.

• Probability Theory
• Random Geometry

Authored book

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

Journal Article

• Many-to-few for non-local branching Markov process
  
  Harris, S. C., Horton, E., Kyprianou, A. E., & Powell, E. (2024). Many-to-few for non-local branching Markov process. Electronic Journal of Probability, 29, Article 41. https://doi.org/10.1214/24-ejp1098
• Thick points of the planar GFF are totally disconnected for all γ≠0
  
  Aru, J., Papon, L., & Powell, E. (2023). Thick points of the planar GFF are totally disconnected for all γ≠0. Electronic Journal of Probability, 28, 1-24. https://doi.org/10.1214/23-ejp975
• Brownian half‐plane excursion and critical Liouville quantum gravity
  
  Aru, J., Holden, N., Powell, E., & Sun, X. (2023). Brownian half‐plane excursion and critical Liouville quantum gravity. Journal of the London Mathematical Society, 107(1), 441-509. https://doi.org/10.1112/jlms.12689
• A characterisation of the continuum Gaussian free field in arbitrary dimensions
  
  Aru, J., & Powell, E. (2022). A characterisation of the continuum Gaussian free field in arbitrary dimensions. Journal De l’École Polytechnique — Mathématiques, 9, 1101-1120. https://doi.org/10.5802/jep.201
• Conformal welding for critical Liouville quantum gravity
  
  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
• Critical Gaussian multiplicative chaos: a review
  
  Powell, E. (2021). Critical Gaussian multiplicative chaos: a review. Markov Processes and Related Fields, 27(4), 557-606.
• (1+𝜀) moments suffice to characterise the GFF
  
  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
• A characterisation of the Gaussian free field
  
  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
• Liouville measure as a multiplicative cascade via level sets of the Gaussian free field
  
  Aru, J., Powell, E., & Sepúlveda, A. (2020). Liouville measure as a multiplicative cascade via level sets of the Gaussian free field. Annales De l’Institut Fourier, 70(1), 245-205. https://doi.org/10.5802/aif.3312
• An invariance principle for branching diffusions in bounded domains
  
  Powell, E. (2019). An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields, 173(3-4), 999-1062. https://doi.org/10.1007/s00440-018-0847-8
• Critical Liouville measure as a limit of subcritical measures
  
  Aru, J., Powell, E., & Sepúlveda, A. (2019). Critical Liouville measure as a limit of subcritical measures. Electronic Communications in Probability, 24, Article 18. https://doi.org/10.1214/19-ecp209
• Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation
  
  Powell, E. (2018). Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electronic Journal of Probability, 23, Article 31. https://doi.org/10.1214/18-ejp157
• Level lines of the Gaussian free field with general boundary data
  
  Powell, E., & Wu, H. (2017). Level lines of the Gaussian free field with general boundary data. Annales De l’Institut Henri Poincaré, Probabilités Et Statistiques, 53(4), 2229-2259. https://doi.org/10.1214/16-aihp789