{"id":"openai-math/Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks","pdf":"https://github.com/openai/math/blob/main/preprints/Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks-September-26-2026","tags":["probability","self-avoiding-walks","statistical-mechanics"],"score":0,"title":"Polynomial vacuum representations and bridge mass for honeycomb walks","domain":"Probability and statistical mechanics","family":"237","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that, under the all-length critical measure, a honeycomb bridge crossing a strip of h layers, with its initial port fixed and its terminal port free, has mean length $`h^{4/3+o(1)}`$. We also obtain central visit probability $`R^{-2/3+o(1)}`$ and mean length $`R^{4/3+o(1)}`$ for macroscopic free-boundary chords in a regular hexagon.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"The three-quarter exponent for honeycomb self-avoiding walk"}