$SLE(κ,ρ)$ processes, hiding exponents and self-avoiding walks in a wedge

Deutscher, Nathan; Batchelor, Murray T.

$SLE(κ,ρ)$ processes, hiding exponents and self-avoiding walks in a wedge

Authors

Description

This article employs Schramm-Loewner Evolution to obtain intersection exponents for several chordal $SLE_{8/3}$ curves in a wedge. As $SLE_{8/3}$ is believed to describe the continuum limit of self-avoiding walks, these exponents correspond to those obtained by Cardy, Duplantier and Saleur for self-avoiding walks in an arbitrary wedge-shaped geometry using conformal invariance based arguments. Our approach builds on work by Werner, where the restriction property for $SLE(κ,ρ)$ processes and an absolute continuity relation allow the calculation of such exponents in the half-plane. Furthermore, the method by which these results are extended is general enough to apply to the new class of hiding exponents introduced by Werner.
12 pages, 3 figures