  In this note we show that a bounded degree planar triangulation is recurrent
if and only if the set of accumulation points of some/any circle packing of it
is polar (that is, planar Brownian motion avoids it with probability 1). This
generalizes a theorem of He and Schramm [6] who proved it when the set of
accumulation points is either empty or a Jordan curve, in which case the graph
has one end. We also show that this statement holds for any straight-line
embedding with angles uniformly bounded away from 0.

Probability