Conformal restriction and related questions

2005/01/01 by Wendelin Werner · 2 citations
Mathematics · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Mathematics #Conformal map #Heuristic #Mathematics education #Combinatorics #Mathematical analysis #Mathematical optimization

paper · pdf · doi:10.1214/154957805100000113

openalex publication_date 2005/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

This survey paper is based on mini-courses given in July 2003 at the University of St-Andrews, and at the ICMS in Edinburgh. Its goal is to give a self-contained and heuristic overview of the recent (i.e. pre-2003) results concerning conformal restriction properties for random planar curves.

Citations

• FRACTAL STRUCTURE OF 2d—QUANTUM GRAVITY
• Infinite conformal symmetry in two-dimensional quantum field theory
• Generating random spanning trees more quickly than the cover time
• Scaling limits of loop-erased random walks and uniform spanning trees
• The Fractal Geometry of Nature
• The Dimension of the Planar Brownian Frontier is 4/3
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Conformal invariance of planar loop-erased random walks and uniform spanning trees

Cited by

• Conformally invariant scaling limits: an overview and a collection of problems
• Schramm–Loewner evolution [wikipedia]