PDE and mathematical physics · Oct 6, 2026
The three-quarter exponent for honeycomb self-avoiding walk
Proves the diameter form of Nienhuis's predicted three-quarter exponent: a uniformly chosen n-step self-avoiding walk on the honeycomb lattice has diameter . Its local mass and covering numbers have exponent 4/3. These estimates hold at every sufficiently large fixed length, simultaneously across scales, with arbitrarily high polynomial probability.
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