Last Branching in Directed Last Passage Percolation

TL;DR

This paper investigates the last branching point in directed polymers within a Poisson environment, revealing its relation to transversal fluctuation exponents and analyzing branch density.

Contribution

It establishes the connection between the last branching point and the transversal fluctuation exponent in directed last passage percolation.

Findings

Last branching point governed by transversal fluctuation exponent

Density of branches analyzed

Provides insights into polymer structure in random environments

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.