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

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

2007-09-13

arxiv.org/abs/0709.2002v1

J. Phys. A 41 (2008) 035001

Physics

Mathematical Physics

12 pages, 3 figures

Scientific paper

10.1088/1751-8113/41/3/035001

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 $SLE(\kappa,\rho)$ 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.

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