Cap-selected amplitudes and triangle chords for honeycomb walks
At the critical honeycomb fugacity, self-avoiding port-to-port chords in an equilateral lattice triangle of side R , summed over both boundary endpoints and restricted to diameter at least $R/100$, have partition sum comparable to R 3/4 and mean length $R^{4/3+o(1)}$. We also determine the amplitude selected by two vacuum caps on a cylinder of circumference N and prove that it grows as $N^{1/6+o(1)}$.
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