The rescaled area-tilted non-crossing random walk line ensemble with a growing number of walks and high boundary conditions converges to the infinite-volume Brownian Gibbs measure μ_{a,b}.
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Scaling limit and tail bounds for a random walk model of SOS level lines
The rescaled area-tilted non-crossing random walk line ensemble with a growing number of walks and high boundary conditions converges to the infinite-volume Brownian Gibbs measure μ_{a,b}.