Gaussian Free Field and Liouville Quantum Gravity

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.

• 1. Definition and properties of the GFF; 2. Liouville measure; 3. Gaussian multiplicative chaos; 4. Statistical physics on random planar maps; 5. Introduction to Liouville conformal field theory; 6. Gaussian free field with Neumann boundary conditions; 7. Quantum wedges and scale-invariant random surfaces; 8. SLE and the quantum zipper; 9. Liouville quantum gravity as a mating of trees; A. Chordal Loewner chains and chordal SLE; B. Reverse Loewner flow and reverse SLE; C. Radial Loewner chains and radial SLE; D. Convergence of random variables in the space of distributions; References; Notation and symbols; Subject index.

'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