Counting paths in the honeycomb lattice

Martin Klazar

Abstract

I will report on the recent remarkable theorem of Duminil-Copin and Smirnov (http://arxiv.org/abs/1007.0575) that the number of paths with length n and start at the origin in the honeycomb lattice (the 3-regular plane graph with hexagonal faces) has asymptotics c^{n+o(n)} where c=2cos(pi/8)=sqrt{2+sqrt{2}}=1.84775... .