SLE(κ,ρ) martingales and duality

2003/03/31 by Julien Dubédat, Julien Dubedat · 5 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60G17 #msc:60G52 #msc:60K35.

paper · pdf · doi:10.1214/009117904000000793

published as Annals of Probability 2005, Vol. 33, No. 1, 223-243 · Published at http://dx.doi.org/10.1214/009117904000000793 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/01/01 · arxiv created 2005/04/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

Various features of the two-parameter family of Schramm–Loewner evolutions SLE (κ,ρ) are studied. In particular, we derive certain restriction properties that lead to a “strong duality” conjecture, which is an identity in law between the outer boundary of a variant of the SLE (κ) process for κ≥4 and a variant of the SLE (16/κ) process.

Citations

• Hausdorff dimensions for SLE6

Cited by

• Onsager--Machlup functional for multiple SLEs
• SLE(κ, ρ) processes, hiding exponents and self-avoiding walks in a wedge
• Stochastic geometry of critical curves, Schramm–Loewner evolutions and conformal field theory
• The scaling limit of two cluster boundaries in critical lattice models
• The correlator toolbox, metrics and moduli

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• Duality of Schramm-Loewner Evolutions
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