Multiple geodesics with the same direction
  The directed last-passage percolation (LPP) model with independent exponential times is considered. We complete the study of asymptotic directions of infinite geodesics, started by Ferrari and Pimentel \cite{FP}. In particular, using a recent result of \cite{CH2} and a local modification argument, we prove there is no (random) direction with more than two geodesics with probability 1. 
David Coupier
math.PR