  We prove an identity in distribution between two kinds of partition functions
for the log-gamma directed polymer model: (1) the point-to-point partition
function in a quadrant, (2) the point-to-line partition function in an octant.
As an application, we prove that the point-to-line free energy of the log-gamma
polymer in an octant obeys a phase transition depending on the strength of the
noise along the boundary. This transition of (de)pinning by randomness was
first predicted in physics by Kardar in 1985 and proved rigorously for zero
temperature models by Baik and Rains in 2001. While it is expected to arise
universally for models in the Kardar-Parisi-Zhang universality class, this is
the first positive temperature model for which this transition can be
rigorously established.
