Some recent aspects of random conformally invariant systems

Abstract

These are the lecture notes from a course given in July 2005 at the summer school in Les Houches. We describe some recent results concerning two-dimensional conformally invariant systems. In particular, we discuss conformally invariant measures on loops and conformal loop-ensembles (CLE).

40 pp., Lecture Notes

References in corpus (1)

• The Full Scaling Limit of Two-Dimensional Critical Percolation

Cited by in corpus (13)

• 2D growth processes: SLE and Loewner chains
• On bounded-type thin local sets of the two-dimensional Gaussian free field
• Decomposition of Brownian loop-soup clusters
• Corner percolation on ${\mathbb{Z}}^2$ and the square root of 17
• Ising (Conformal) Fields and Cluster Area Measures
• Towards conformal invariance of 2D lattice models
• SLE(6) and CLE(6) from Critical Percolation
• Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus
• Conformal loop ensembles and the stress-energy tensor. II. Construction of the stress-energy tensor
• Conformal loop ensembles and the stress-energy tensor. I. Fundamental notions of CLE
• Brownian Loops and Conformal Fields
• Universal Behavior of Connectivity Properties in Fractal Percolation Models
• Scaling Limits of Two-Dimensional Percolation: an Overview