Abstract
We prove an invariance principle for a class of tilted 1 + 1-dimensional SOS models or, equivalently, for a class of tilted random walk bridges in \({\mathbb{Z}_+}\). The limiting objects are stationary reversible ergodic diffusions with drifts given by the logarithmic derivatives of the ground states of associated singular Sturm–Liouville operators. In the case of a linear area tilt, we recover the Ferrari–Spohn diffusion with log-Airy drift, which was derived in Ferrari and Spohn (Ann Probab 33(4):1302—1325, 2005) in the context of Brownian motions conditioned to stay above circular and parabolic barriers.
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Communicated by F. Toninelli
D.I. was supported by the Israeli Science Foundation grants 817/09 and 1723/14.
Y.V. was partially supported by the Swiss National Science Foundation.
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Ioffe, D., Shlosman, S. & Velenik, Y. An Invariance Principle to Ferrari–Spohn Diffusions. Commun. Math. Phys. 336, 905–932 (2015). https://doi.org/10.1007/s00220-014-2277-5
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DOI: https://doi.org/10.1007/s00220-014-2277-5