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

• Probability

Authored book

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

Journal Article

• Aru, Juhan & Powell, Ellen (Submitted). A characterisation of the continuum Gaussian free field in dimension d>=2.
• Aru, Juhan, Holden, Nina, Powell, Ellen & Sun, Xin (2023). Brownian half‐plane excursion and critical Liouville quantum gravity. Journal of the London Mathematical Society 107(1 ): 441 - 509.
• Aru, Juhan & Powell, Ellen (2022). A characterisation of the continuum Gaussian free field in arbitrary dimensions. Journal de l’École polytechnique — Mathématiques 9: 1101-1120.
• Holden, Nina & Powell, Ellen (2021). Conformal welding for critical Liouville quantum gravity. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 57(3): 1229-1254.
• Berestycki, Nathanaël, Powell, Ellen & Ray, Gourab (2021). (1+𝜀) moments suffice to characterise the GFF. Electronic Journal of Probability 26: 1-25.
• Powell, Ellen (2021). Critical Gaussian multiplicative chaos: a review. Markov Processes and Related Fields 27(4): 557-606.
• Aru, Juhan, Powell, Ellen & Sepúlveda, Avelio (2020). Liouville measure as a multiplicative cascade via level sets of the Gaussian free field. Annales de l'Institut Fourier 70(1): 205-245.
• Berestycki, Nathanaël, Powell, Ellen & Ray, Gourab (2020). A characterisation of the Gaussian free field. Probability Theory and Related Fields 176(3-4): 1259-1301.
• Aru, Juhan, Powell, Ellen & Sepúlveda, Avelio (2019). Critical Liouville measure as a limit of subcritical measures. Electronic Communications in Probability 24: 18, 1-16.
• Powell, Ellen (2019). An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields 173(3-4): 999-1062.
• Powell, Ellen (2018). Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electronic Journal of Probability 23: 31, 1-26.
• Powell, Ellen & Wu, Hao (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.