Scaling for a One-dimensional Directed Polymer with Boundary Conditions ( Revised )

  title={Scaling for a One-dimensional Directed Polymer with Boundary Conditions ( Revised )},
  author={Timo Sepp{\"a}l{\"a}inen},
We study a 1+1-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers this model is special in the same way as the last-passage percolation model with exponential or geometric weights is special among growth models, namely, both permit explicit calculations. With appropriate boundary conditions the polymer with log-gamma weights satisfies an analogue of Burke’s theorem for queues. Building on this we prove the… CONTINUE READING
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