Directed polymers in random environment are known to concentrate in specific corridors when the disorder is strong. We can analyse this in a precise manner for the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Seppäläinen. In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk.

Francis Comets (U Paris)Tue, Mar 8

Directed polymers in random environment are known to concentrate in specific corridors when the disorder is strong. We can analyse this in a precise manner for the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Seppäläinen. In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk.