Some Relations Between the Directed Polymer Model in a Random Environment and Directed First Passage Percolation
Greg Morrow
University of Colorado, Colorado Springs
In this talk we show various aspects of recent rigorous results for directed polymers. This study provides clues for extending the theory of directed first passage percolation that arises as a limiting case of zero temperature in the interaction of the directed polymer model. In particular we describe the Central Limit Theory for the "height" problem of the directed polymer model. As an application and illustration of subadditivity, we show a bound for the free energy of the directed polymer model (as a function of inverse temperature) that recovers the correct low temperature free energy profile.
