Critical honeycomb chords with prescribed boundary endpoints

Abstract — v2

Critical self-avoiding walks between prescribed, macroscopically separated boundary ports of a regular honeycomb hexagon have length $R^{4/3+o(1)}$ in probability, where R is the scale of the hexagon. We prove the corresponding statements for half-plane arches, parallel cuts and nonparallel pure cuts. The half-plane law also has mean length $R^{4/3+o(1)}$. A separate strip argument gives endpoint mean laws on one density-one set of heights and in an aligned, critically weighted mixture of all even heights in a macroscopic interval.