At the critical honeycomb self-avoiding-walk activity, the total weight of unrooted polygons of diameter at least r is r^{-2+o(1)}, their length-weighted tail is r^{-2/3+o(1)}, and the truncated second-length-moment mass through diameter r is at most r^{2/3+o(1)}.
At the critical honeycomb self-avoiding-walk activity, the total weight of unrooted polygons of diameter at least r is r^{-2+o(1)}, their length-weighted tail is r^{-2/3+o(1)}, and the truncated second-length-moment mass through diameter r is at most r^{2/3+o(1)}.
At the critical honeycomb self-avoiding-walk activity, the total weight of unrooted polygons of diameter at least r is r^{-2+o(1)}, their length-weighted tail is r^{-2/3+o(1)}, and the truncated second-length-moment mass through diameter r is at most r^{2/3+o(1)}.
If correct, establishes the critical polygon tail laws that yield diameter n^{3/4+o(1)} under length-cutoff ensembles.
What are the critical diameter and length-tail exponents for honeycomb self-avoiding polygons?
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OpenAI reports critical honeycomb polygon diameter-tail exponents
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