{"id":"openai-math/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks","pdf":"https://github.com/openai/math/blob/main/preprints/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026","tags":["probability","combinatorics","random-walks","polymers"],"score":0,"title":"Radial transfer estimates and polygon length laws 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 critical diameter-tail exponents −2 for unrooted honeycomb polygons and −2/3 for length-weighted polygons, together with a truncated second-length-moment bound of exponent 2/3. Consequently, polygons conditioned to have length at least n have diameter $`n^{3/4+o(1)}`$ in probability under either weight.","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"}