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}.
Ballot theorems for random walks with finite variance
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abstract
We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold.
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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}.