$SLE(\kappa,\rho)$ processes, hiding exponents and self-avoiding walks in a wedge

TL;DR

This paper uses Schramm-Loewner Evolution to calculate intersection exponents for $SLE_{8/3}$ curves in a wedge, providing insights into self-avoiding walks and introducing a new class of hiding exponents.

Contribution

It extends the application of $SLE( ho)$ processes to wedge geometries and introduces a method to compute new hiding exponents for these processes.

Findings

Calculated intersection exponents for $SLE_{8/3}$ in wedges.

Connected $SLE_{8/3}$ exponents to self-avoiding walks.

Extended the restriction property to a new class of hiding exponents.

Abstract

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.