Critical exponents for two-dimensional percolation

2001/01/01 by Stanislav Smirnov, Wendelin Werner · 3 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Random Matrices and Applications #Mathematics #Percolation critical exponents #Critical exponent #Percolation (cognitive psychology) #Statistical physics #Scaling #Directed percolation #Lattice (music) #Geometry #Physics

paper · pdf · doi:10.4310/mrl.2001.v8.n6.a4

openalex publication_date 2001/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof of Cardy's formula, in order to determine the existence and value of critical exponents associated to percolation on the triangular lattice.

Citations

• Scaling relations for 2D-percolation
• Scaling limits of loop-erased random walks and uniform spanning trees
• The Dimension of the Planar Brownian Frontier is 4/3
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits

Cited by

• Quantitative noise sensitivity and exceptional times for percolation
• Conformally invariant scaling limits: an overview and a collection of problems
• Schramm–Loewner evolution [wikipedia]