Last Branching in Directed Last Passage Percolation,

#### Pablo A. Ferrari, H. Spohn

2003, v.9, №2, 323-339

ABSTRACT

The $1+1$ dimensional directed polymers in a Poissonean random environment is studied. For two polymers of maximal length with the same origin and distinct end points we establish that the point of last branching is governed by the exponent for the transversal fluctuations of a single polymer. We also investigate the density of branches.

Keywords: first passage percolation