Gaussian Free Field and Liouville Quantum Gravity

‘Beautifully written and illustrated, this is a perfect introduction for anyone with a graduate-level probability background who wants to learn more about Gaussian free fields, random surfaces, conformal field theory, Liouville quantum gravity, SLE and the surrounding circle of ideas. The authors have spent years perfecting this exposition. I highly recommend this book to my own graduate students – and to interested researchers at any level.’ Scott Sheffield, Massachusetts Institute of Technology‘For a technically difficult research area with a large body of literature it is essential to have a clean and pedagogical introductory text. Berestycki and Powell’s book fills exactly this need and it has been a tremendous help for all my students while learning this research area. Additionally, the book has quickly become a standard reference and it’s an excellent text for looking up key facts of our field.’ Nina Holden, New York University‘Berestycki and Powell succeed brilliantly in making the rapidly evolving field of Liouville Quantum Gravity accessible to the probability community. There is no better place to learn the basics of the theories of Gaussian Free Field and Multiplicative Chaos than this book and no better introduction to the recent research in Liouville CFT and its connections to SLE.’ Antti Kupiainen, University of Helsinki

Nathanaël Berestycki has held the Chair of Stochastics at the University of Vienna since 2018. He has been an associate editor of numerous journals, including the ‘Annals of Probability’, and was an invited speaker at the International Congress of Mathematical Physics (ICMP) in 2024.

Ellen Powell is Associate Professor in the probability group at Durham University, where she has been since 2019.