Natural parametrization of SLE: the Gaussian free field point of view

DOI10.1214/18-EJP232zbMath1402.60102arXiv1708.03801MaRDI QIDQ1994509

Stéphane Benoist

Publication date: 1 November 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03801

zbMATH Keywords

SLEGaussian free fieldLQGnatural parametrizationGFF

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (13)

Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity ⋮ Introduction to the Liouville quantum gravity metric ⋮ Brownian half‐plane excursion and critical Liouville quantum gravity ⋮ The Minkowski content measure for the Liouville quantum gravity metric ⋮ Equivalence of Liouville measure and Gaussian free field ⋮ Conformal welding of quantum disks ⋮ The SLE loop via conformal welding of quantum disks ⋮ A Gaussian free field approach to the natural parametrisation of \(\mathrm{SLE}_4\) ⋮ Anomalous diffusion of random walk on random planar maps ⋮ External diffusion-limited aggregation on a spanning-tree-weighted random planar map ⋮ Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines ⋮ Conformal welding for critical Liouville quantum gravity ⋮ Connectivity properties of the adjacency graph of \(\text{SLE}_{\kappa}\) bubbles for \(\kappa\in(4,8)\)

Cites Work

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• Conformal weldings of random surfaces: SLE and the quantum gravity zipper
• Gaussian multiplicative chaos and applications: a review
• Quantum Loewner evolution
• Intersections of SLE paths: the double and cut point dimension of SLE
• Liouville quantum gravity and KPZ
• A natural parametrization for the Schramm-Loewner evolution
• The dimension of the SLE curves
• Almost sure multifractal spectrum for the tip of an SLE curve
• Minkowski content and natural parameterization for the Schramm-Loewner evolution
• An elementary approach to Gaussian multiplicative chaos

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