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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. These models are motivated by a range of physical applications, particularly stemming from materials science. I also like working with branching structures, especially when they appear in connection with the above models!
Simulation of the discrete planar Gaussian free field
Books & Notes
Books & Notes
Gaussian free field and Liouville quantum gravity with Nathanaël Berestycki. To be published by Cambridge University Press.
Lecture notes on the Gaussian free field with Wendelin Werner. Cours Spécialisés 28, Société Mathématique de France, (2022).
Papers
Papers
Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc with Alex Watson and William Da Silva.
Stability of (sub)critical non-local spatial branching processes with and without immigration with Emma Horton, Andreas Kyprianou, Pedro Martín-Chávez, Victor Rivero. Submitted.
An elementary approach to quantum length of SLE with Avelio Sepúlveda. Submitted.
Many to few for non-local branching Markov processes with Simon Harris, Emma Horton and Andreas Kyprianou. Electronic Journal of Probability. Vol 29, p1 - 26 (2024).
Thick points of the planar GFF are totall disconnected for all \gamma\ne 0 with Juhan Aru and Léonie Papon. Electronic Journal of Probability. Vol 28, paper no.85, p1-28 (2023).
Brownian half-plane excursion and critical Liouville quantum gravity with Juhan Aru, Nina Holden and Xin Sun. Journal of the London Mathematical Society. Vol 107, Issue 1, p441-509 (2023).
A characterisation of the continuum Gaussian free field in dimension d>=2 with Juhan Aru. Journal de l’École polytechnique — Mathématiques, Vol 9, p1101-1120 (2022).
Critical Gaussian multiplicative chaos: a review. Markov Processes and Related Fields. Vol 27, p557–606 (2021).
(1+ε)-moments suffice to characterise the GFF with Nathanaël Berestycki and Gourab Ray. Electronic Journal of Probability. Vol 26 (2021).
Conformal welding for critical Liouville quantum gravity with Nina Holden. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 57(3): 1229-1254 (2021).
A characterisation of the Gaussian free field with Nathanaël Berestycki and Gourab Ray. Probability Theory and Related Fields. Vol 176, p1259–1301 (2020).
Liouville measure as a multiplicative cascade via level sets of the Gaussian free field with Juhan Aru and Avelio Sepúlveda. Annales de l'institut Fourier. Vol 70, No. 1, p205-245 (2020).
Critical Liouville measure as a limit of subcritical measures with Juhan Aru and Avelio Sepúlveda. Electronic Communications in Proability. Vol 24 (2019).
An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields, Vol 173, p999-1062 (2019).
Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electronic Journal of Probability. Vol 23, paper no.31, p1-26 (2018). (Note there is an error with Lemma 2.3 in the journal version. See link here for corrected article!)
Level lines of the Gaussian free field with general boundary data with Hao Wu. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Vol. 53, No. 4, p2229–2259 (2017).
Collaborators: Juhan Aru, Nathanaël Berestycki, William Da Silva, Simon Harris, Nina Holden, Emma Horton, Andreas Kyprianou, Pedro Martín-Chávez, Léonie Papon, Gourab Ray, Avelio Sepúlveda, Xin Sun, Victor Rivero, Alex Watson, Wendelin Werner, Hao Wu.
Other
Other
Multifractal random measures (an article for the LMS newsletter).
Recent Talks
Recent Talks
Brownian half plane excursions, CLE and critical Liouville quantum gravity (video)
out.mp4This simulation, made by Henry Jackson, is a binary branching Brownian motion in the disc with killing at the boundary. This is (a particular version of) the main object of interest in the first paper listed above. In the simulation different coloured paths represent different particles.
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